diff --git a/.github/workflows/i386.yml b/.github/workflows/i386.yml
new file mode 100644
index 000000000000..4a4d65b25b61
--- /dev/null
+++ b/.github/workflows/i386.yml
@@ -0,0 +1,39 @@
+name: XGBoost-i386-test
+
+on: [push, pull_request]
+
+permissions:
+  contents: read # to fetch code (actions/checkout)
+
+jobs:
+  build-32bit:
+    name: Build 32-bit
+    runs-on: ubuntu-latest
+    services:
+      registry:
+        image: registry:2
+        ports:
+          - 5000:5000
+    steps:
+    - uses: actions/checkout@v2.5.0
+      with:
+        submodules: 'true'
+    - name: Set up Docker Buildx
+      uses: docker/setup-buildx-action@v3
+      with:
+        driver-opts: network=host
+    - name: Build and push container
+      uses: docker/build-push-action@v5
+      with:
+        context: .
+        file: tests/ci_build/Dockerfile.i386
+        push: true
+        tags: localhost:5000/xgboost/build-32bit:latest
+        cache-from: type=gha
+        cache-to: type=gha,mode=max
+    - name: Build XGBoost
+      run: |
+        docker run --rm -v $PWD:/workspace -w /workspace \
+          -e CXXFLAGS='-Wno-error=overloaded-virtual -Wno-error=maybe-uninitialized -Wno-error=redundant-move' \
+          localhost:5000/xgboost/build-32bit:latest \
+          tests/ci_build/build_via_cmake.sh
diff --git a/CMakeLists.txt b/CMakeLists.txt
index 4f240e806282..dbfa1cdc225b 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -39,9 +39,6 @@ elseif(CMAKE_CXX_COMPILER_ID STREQUAL "Clang")
     message(FATAL_ERROR "Need Clang 9.0 or newer to build XGBoost")
   endif()
 endif()
-if(CMAKE_SIZE_OF_VOID_P EQUAL 4)
-  message(FATAL_ERROR "XGBoost does not support 32-bit archs. Please use 64-bit arch instead.")
-endif()
 
 include(${xgboost_SOURCE_DIR}/cmake/PrefetchIntrinsics.cmake)
 find_prefetch_intrinsics()
diff --git a/src/c_api/c_api.cc b/src/c_api/c_api.cc
index d4cc217d1ee8..0f4748bfec27 100644
--- a/src/c_api/c_api.cc
+++ b/src/c_api/c_api.cc
@@ -1,5 +1,5 @@
 /**
- * Copyright 2014-2023 by XGBoost Contributors
+ * Copyright 2014-2024 by XGBoost Contributors
  */
 #include "xgboost/c_api.h"
 
@@ -991,8 +991,8 @@ XGB_DLL int XGBoosterBoostOneIter(BoosterHandle handle, DMatrixHandle dtrain, bs
   auto *learner = static_cast<Learner *>(handle);
   auto ctx = learner->Ctx()->MakeCPU();
 
-  auto t_grad = linalg::MakeTensorView(&ctx, common::Span{grad, len}, len);
-  auto t_hess = linalg::MakeTensorView(&ctx, common::Span{hess, len}, len);
+  auto t_grad = linalg::MakeTensorView(&ctx, common::Span{grad, static_cast<size_t>(len)}, len);
+  auto t_hess = linalg::MakeTensorView(&ctx, common::Span{hess, static_cast<size_t>(len)}, len);
 
   auto s_grad = linalg::ArrayInterfaceStr(t_grad);
   auto s_hess = linalg::ArrayInterfaceStr(t_hess);
diff --git a/src/common/column_matrix.h b/src/common/column_matrix.h
index 0862c21ad1fd..440f3c0a87c8 100644
--- a/src/common/column_matrix.h
+++ b/src/common/column_matrix.h
@@ -1,5 +1,5 @@
 /**
- * Copyright 2017-2023, XGBoost Contributors
+ * Copyright 2017-2024, XGBoost Contributors
  * \file column_matrix.h
  * \brief Utility for fast column-wise access
  * \author Philip Cho
@@ -176,7 +176,7 @@ class ColumnMatrix {
     void SetValid(typename LBitField32::index_type i) { missing.Clear(i); }
     /** @brief assign the storage to the view. */
     void InitView() {
-      missing = LBitField32{Span{storage.data(), storage.size()}};
+      missing = LBitField32{Span{storage.data(), static_cast<size_t>(storage.size())}};
     }
 
     void GrowTo(std::size_t n_elements, bool init) {
@@ -318,8 +318,8 @@ class ColumnMatrix {
     common::Span<const BinIdxType> bin_index = {
         reinterpret_cast<const BinIdxType*>(&index_[feature_offset * bins_type_size_]),
         column_size};
-    return std::move(DenseColumnIter<BinIdxType, any_missing>{
-        bin_index, static_cast<bst_bin_t>(index_base_[fidx]), missing_.missing, feature_offset});
+    return DenseColumnIter<BinIdxType, any_missing>{
+        bin_index, static_cast<bst_bin_t>(index_base_[fidx]), missing_.missing, feature_offset};
   }
 
   // all columns are dense column and has no missing value
@@ -332,7 +332,7 @@ class ColumnMatrix {
     DispatchBinType(bins_type_size_, [&](auto t) {
       using ColumnBinT = decltype(t);
       auto column_index = Span<ColumnBinT>{reinterpret_cast<ColumnBinT*>(index_.data()),
-                                           index_.size() / sizeof(ColumnBinT)};
+                                           static_cast<size_t>(index_.size() / sizeof(ColumnBinT))};
       ParallelFor(n_samples, n_threads, [&](auto rid) {
         rid += base_rowid;
         const size_t ibegin = rid * n_features;
diff --git a/src/common/hist_util.h b/src/common/hist_util.h
index fbbd15b49fb5..e829752dae3d 100644
--- a/src/common/hist_util.h
+++ b/src/common/hist_util.h
@@ -1,5 +1,5 @@
 /**
- * Copyright 2017-2023 by XGBoost Contributors
+ * Copyright 2017-2024 by XGBoost Contributors
  * \file hist_util.h
  * \brief Utility for fast histogram aggregation
  * \author Philip Cho, Tianqi Chen
@@ -113,8 +113,8 @@ class HistogramCuts {
     auto end = ptrs[column_id + 1];
     auto beg = ptrs[column_id];
     auto it = std::upper_bound(values.cbegin() + beg, values.cbegin() + end, value);
-    auto idx = it - values.cbegin();
-    idx -= !!(idx == end);
+    auto idx = static_cast<bst_bin_t>(it - values.cbegin());
+    idx -= !!(idx == static_cast<bst_bin_t>(end));
     return idx;
   }
 
@@ -136,8 +136,8 @@ class HistogramCuts {
     auto beg = ptrs[fidx] + vals.cbegin();
     // Truncates the value in case it's not perfectly rounded.
     auto v = static_cast<float>(common::AsCat(value));
-    auto bin_idx = std::lower_bound(beg, end, v) - vals.cbegin();
-    if (bin_idx == ptrs.at(fidx + 1)) {
+    auto bin_idx = static_cast<bst_bin_t>(std::lower_bound(beg, end, v) - vals.cbegin());
+    if (bin_idx == static_cast<bst_bin_t>(ptrs.at(fidx + 1))) {
       bin_idx -= 1;
     }
     return bin_idx;
diff --git a/src/common/ref_resource_view.h b/src/common/ref_resource_view.h
index d4f82e615c6f..61adfdb7bea8 100644
--- a/src/common/ref_resource_view.h
+++ b/src/common/ref_resource_view.h
@@ -1,5 +1,5 @@
 /**
- * Copyright 2023, XGBoost Contributors
+ * Copyright 2023-2024, XGBoost Contributors
  */
 #ifndef XGBOOST_COMMON_REF_RESOURCE_VIEW_H_
 #define XGBOOST_COMMON_REF_RESOURCE_VIEW_H_
@@ -76,7 +76,7 @@ class RefResourceView {
 
   [[nodiscard]] size_type size() const { return size_; }  // NOLINT
   [[nodiscard]] size_type size_bytes() const {            // NOLINT
-    return Span<const value_type>{data(), size()}.size_bytes();
+    return Span<const value_type>{data(), static_cast<size_t>(size())}.size_bytes();
   }
   [[nodiscard]] value_type* data() { return ptr_; };              // NOLINT
   [[nodiscard]] value_type const* data() const { return ptr_; };  // NOLINT
diff --git a/src/data/gradient_index.cc b/src/data/gradient_index.cc
index 1d3faf94532e..88a38d5cce74 100644
--- a/src/data/gradient_index.cc
+++ b/src/data/gradient_index.cc
@@ -1,5 +1,5 @@
 /**
- * Copyright 2017-2023, XGBoost Contributors
+ * Copyright 2017-2024, XGBoost Contributors
  * \brief Data type for fast histogram aggregation.
  */
 #include "gradient_index.h"
@@ -148,7 +148,8 @@ void GHistIndexMatrix::ResizeIndex(const size_t n_index, const bool isDense) {
       new_vec = {new_ptr, n_bytes / sizeof(std::uint8_t), malloc_resource};
     }
     this->data = std::move(new_vec);
-    this->index = common::Index{common::Span{data.data(), data.size()}, t_size};
+    this->index = common::Index{common::Span{data.data(), static_cast<size_t>(data.size())},
+        t_size};
   };
 
   if ((MaxNumBinPerFeat() - 1 <= static_cast<int>(std::numeric_limits<uint8_t>::max())) &&
diff --git a/src/data/gradient_index_format.cc b/src/data/gradient_index_format.cc
index fa8f492ed12a..542d3aaebda7 100644
--- a/src/data/gradient_index_format.cc
+++ b/src/data/gradient_index_format.cc
@@ -1,5 +1,5 @@
 /**
- * Copyright 2021-2023 XGBoost contributors
+ * Copyright 2021-2024 XGBoost contributors
  */
 #include <cstddef>      // for size_t
 #include <cstdint>      // for uint8_t
@@ -40,7 +40,9 @@ class GHistIndexRawFormat : public SparsePageFormat<GHistIndexMatrix> {
       return false;
     }
     // - index
-    page->index = common::Index{common::Span{page->data.data(), page->data.size()}, size_type};
+    page->index =
+        common::Index{common::Span{page->data.data(), static_cast<size_t>(page->data.size())},
+            size_type};
 
     // hit count
     if (!common::ReadVec(fi, &page->hit_count)) {
diff --git a/src/predictor/predictor.cc b/src/predictor/predictor.cc
index aad33c272dc7..019804eda31c 100644
--- a/src/predictor/predictor.cc
+++ b/src/predictor/predictor.cc
@@ -1,5 +1,5 @@
 /**
- * Copyright 2017-2023 by Contributors
+ * Copyright 2017-2024 by Contributors
  */
 #include "xgboost/predictor.h"
 
@@ -46,7 +46,7 @@ void ValidateBaseMarginShape(linalg::Tensor<float, D> const& margin, bst_row_t n
 void Predictor::InitOutPredictions(const MetaInfo& info, HostDeviceVector<bst_float>* out_preds,
                                    const gbm::GBTreeModel& model) const {
   CHECK_NE(model.learner_model_param->num_output_group, 0);
-  std::size_t n{model.learner_model_param->OutputLength() * info.num_row_};
+  auto n = static_cast<size_t>(model.learner_model_param->OutputLength() * info.num_row_);
 
   const HostDeviceVector<bst_float>* base_margin = info.base_margin_.Data();
   if (ctx_->Device().IsCUDA()) {
diff --git a/src/tree/hist/hist_cache.h b/src/tree/hist/hist_cache.h
index 8a2ba193af0c..715e1d73e60c 100644
--- a/src/tree/hist/hist_cache.h
+++ b/src/tree/hist/hist_cache.h
@@ -1,5 +1,5 @@
 /**
- * Copyright 2023 by XGBoost Contributors
+ * Copyright 2023-2024 by XGBoost Contributors
  */
 #ifndef XGBOOST_TREE_HIST_HIST_CACHE_H_
 #define XGBOOST_TREE_HIST_HIST_CACHE_H_
@@ -48,11 +48,13 @@ class BoundedHistCollection {
   BoundedHistCollection() = default;
   common::GHistRow operator[](std::size_t idx) {
     auto offset = node_map_.at(idx);
-    return common::Span{data_->data(), data_->size()}.subspan(offset, n_total_bins_);
+    return common::Span{data_->data(), static_cast<size_t>(data_->size())}.subspan(
+        offset, n_total_bins_);
   }
   common::ConstGHistRow operator[](std::size_t idx) const {
     auto offset = node_map_.at(idx);
-    return common::Span{data_->data(), data_->size()}.subspan(offset, n_total_bins_);
+    return common::Span{data_->data(), static_cast<size_t>(data_->size())}.subspan(
+        offset, n_total_bins_);
   }
   void Reset(bst_bin_t n_total_bins, std::size_t n_cached_nodes) {
     n_total_bins_ = n_total_bins;
diff --git a/tests/ci_build/Dockerfile.i386 b/tests/ci_build/Dockerfile.i386
new file mode 100644
index 000000000000..d7c133e2aee4
--- /dev/null
+++ b/tests/ci_build/Dockerfile.i386
@@ -0,0 +1,8 @@
+FROM i386/debian:sid
+
+ENV DEBIAN_FRONTEND noninteractive
+SHELL ["/bin/bash", "-c"]   # Use Bash as shell
+
+RUN \
+    apt-get update && \
+    apt-get install -y tar unzip wget git build-essential ninja-build cmake
diff --git a/tests/cpp/c_api/test_c_api.cc b/tests/cpp/c_api/test_c_api.cc
index 4491dee92de5..c4c1f0c45f42 100644
--- a/tests/cpp/c_api/test_c_api.cc
+++ b/tests/cpp/c_api/test_c_api.cc
@@ -1,5 +1,5 @@
 /**
- * Copyright 2019-2023 XGBoost contributors
+ * Copyright 2019-2024 XGBoost contributors
  */
 #include <gtest/gtest.h>
 #include <xgboost/c_api.h>
@@ -212,8 +212,8 @@ TEST(CAPI, JsonModelIO) {
   bst_ulong saved_len{0};
   XGBoosterSaveModelToBuffer(handle, R"({"format": "ubj"})", &saved_len, &saved);
   ASSERT_EQ(len, saved_len);
-  auto l = StringView{data, len};
-  auto r = StringView{saved, saved_len};
+  auto l = StringView{data, static_cast<size_t>(len)};
+  auto r = StringView{saved, static_cast<size_t>(saved_len)};
   ASSERT_EQ(l.size(), r.size());
   ASSERT_EQ(l, r);
 
diff --git a/tests/cpp/helpers.cc b/tests/cpp/helpers.cc
index 97db9dbd87fc..6ce362f46763 100644
--- a/tests/cpp/helpers.cc
+++ b/tests/cpp/helpers.cc
@@ -1,5 +1,5 @@
 /**
- * Copyright 2016-2023 by XGBoost contributors
+ * Copyright 2016-2024 by XGBoost contributors
  */
 #include "helpers.h"
 
@@ -216,7 +216,7 @@ SimpleLCG::StateType SimpleLCG::Max() const { return max(); }
 static_assert(SimpleLCG::max() - SimpleLCG::min());
 
 void RandomDataGenerator::GenerateLabels(std::shared_ptr<DMatrix> p_fmat) const {
-  RandomDataGenerator{p_fmat->Info().num_row_, this->n_targets_, 0.0f}.GenerateDense(
+  RandomDataGenerator{static_cast<bst_row_t>(p_fmat->Info().num_row_), this->n_targets_, 0.0f}.GenerateDense(
       p_fmat->Info().labels.Data());
   CHECK_EQ(p_fmat->Info().labels.Size(), this->rows_ * this->n_targets_);
   p_fmat->Info().labels.Reshape(this->rows_, this->n_targets_);
@@ -458,7 +458,7 @@ void RandomDataGenerator::GenerateCSR(
   EXPECT_EQ(row_count, dmat->Info().num_row_);
 
   if (with_label) {
-    RandomDataGenerator{dmat->Info().num_row_, this->n_targets_, 0.0f}.GenerateDense(
+    RandomDataGenerator{static_cast<bst_row_t>(dmat->Info().num_row_), this->n_targets_, 0.0f}.GenerateDense(
         dmat->Info().labels.Data());
     CHECK_EQ(dmat->Info().labels.Size(), this->rows_ * this->n_targets_);
     dmat->Info().labels.Reshape(this->rows_, this->n_targets_);
diff --git a/tests/cpp/helpers.h b/tests/cpp/helpers.h
index 9adda8aedfad..d603685eb073 100644
--- a/tests/cpp/helpers.h
+++ b/tests/cpp/helpers.h
@@ -1,5 +1,5 @@
 /**
- * Copyright 2016-2023 by XGBoost contributors
+ * Copyright 2016-2024 by XGBoost contributors
  */
 #pragma once
 
@@ -238,7 +238,7 @@ class RandomDataGenerator {
 
   bst_bin_t bins_{0};
   std::vector<FeatureType> ft_;
-  bst_cat_t max_cat_;
+  bst_cat_t max_cat_{32};
 
   Json ArrayInterfaceImpl(HostDeviceVector<float>* storage, size_t rows, size_t cols) const;