diff --git a/tests/unit/test_utils.py b/tests/unit/test_utils.py
index 22655866a0..258f74e567 100644
--- a/tests/unit/test_utils.py
+++ b/tests/unit/test_utils.py
@@ -1854,3 +1854,25 @@ def test_render_command_report_minimal():
         label='foo'
         )) == """## foo
 """
+
+
+def test_retry_strategy_github_rate_limits(monkeypatch):
+    """ Test GitHub rate limit handling in RetryStrategy """
+    strategy = tmt.utils.RetryStrategy()
+    mock_time = unittest.mock.MagicMock()
+    monkeypatch.setattr('time.time', mock_time)
+    mock_time.return_value = 1704114000  # Example: 2024-01-01 13:00:00 UTC
+    mock_sleep = unittest.mock.MagicMock()
+    monkeypatch.setattr('time.sleep', mock_sleep)
+
+    # Test primary rate limit
+    mock_response = unittest.mock.MagicMock()
+    mock_response.status_code = 403
+    mock_response.headers = {
+        'X-GitHub-Request-Id': 'ABC123',
+        'X-RateLimit-Remaining': '0',
+        'X-RateLimit-Reset': '1704114100'  # 2024-01-01 13:01:40 UTC (100 seconds later)
+        }
+
+    strategy.increment(error=None, response=mock_response)
+    mock_sleep.assert_called_once_with(100)  # Should wait 100 seconds until reset time
diff --git a/tmt/utils/__init__.py b/tmt/utils/__init__.py
index c1b258ba8d..072db75b02 100644
--- a/tmt/utils/__init__.py
+++ b/tmt/utils/__init__.py
@@ -4358,6 +4358,30 @@ def increment(
 
                 raise GeneralError(message) from error
 
+        # Handle GitHub-specific responses
+        # https://docs.github.com/en/rest/using-the-rest-api/rate-limits-for-the-rest-api?apiVersion=2022-11-28#exceeding-the-rate-limit
+        response = cast(requests.Response, kwargs.get('response'))
+        if response is not None and 'X-GitHub-Request-Id' in response.headers:
+            headers = response.headers
+
+            # Handle rate limiting
+            if response.status_code in (403, 429):
+                # Primary rate limit exceeded
+                if ('X-RateLimit-Remaining' in headers and
+                        int(headers['X-RateLimit-Remaining']) == 0):
+                    reset_time = int(headers['X-RateLimit-Reset'])
+                    # Wait until the rate limit resets
+                    wait_time = reset_time - int(time.time())
+                    if wait_time > 0:
+                        time.sleep(wait_time)
+                        return super().increment(*args, **kwargs)
+
+                # Secondary rate limit - respect Retry-After if provided
+                if 'Retry-After' in headers:
+                    retry_after = int(headers['Retry-After'])
+                    time.sleep(retry_after)
+                    return super().increment(*args, **kwargs)
+
         return super().increment(*args, **kwargs)