diff --git a/Tests/RunCMake/CMakeLists.txt b/Tests/RunCMake/CMakeLists.txt
index c92aac1484..e8fc9dad84 100644
--- a/Tests/RunCMake/CMakeLists.txt
+++ b/Tests/RunCMake/CMakeLists.txt
@@ -747,6 +747,7 @@ add_RunCMake_test(set_property)
 add_RunCMake_test(string
   -DCMAKE_SYSTEM_NAME=${CMAKE_SYSTEM_NAME}
   -DCMAKE_SYSTEM_PROCESSOR=${CMAKE_SYSTEM_PROCESSOR}
+  -DCMake_TEST_NO_64BIT_TIME=${CMake_TEST_NO_64BIT_TIME}
   )
 add_RunCMake_test(test_include_dirs)
 add_RunCMake_test(BundleUtilities)
diff --git a/Tests/RunCMake/string/RunCMakeTest.cmake b/Tests/RunCMake/string/RunCMakeTest.cmake
index 6baf6214fc..b0aabb6ca2 100644
--- a/Tests/RunCMake/string/RunCMakeTest.cmake
+++ b/Tests/RunCMake/string/RunCMakeTest.cmake
@@ -23,6 +23,7 @@ run_cmake(JoinNoVar)
 run_cmake(Timestamp)
 if(NOT CMAKE_SYSTEM_NAME STREQUAL "AIX" # FIXME: Needs 64-bit build
     AND NOT CMAKE_SYSTEM_NAME STREQUAL "SunOS" # FIXME: Needs 64-bit build
+    AND NOT CMake_TEST_NO_64BIT_TIME
     )
   run_cmake(Timestamp2038)
 endif()
diff --git a/bootstrap b/bootstrap
index 2ec6aacca7..d88a88db96 100755
--- a/bootstrap
+++ b/bootstrap
@@ -1848,7 +1848,7 @@ fi
 system_flags=''
 case "${cmake_system}" in
   # Ensure filesystem access uses 64-bit offsets even on 32-bit hosts.
-  *Linux*) system_flags='-D_FILE_OFFSET_BITS=64' ;;
+  *Linux*) system_flags='-D_FILE_OFFSET_BITS=64 -D_TIME_BITS=64' ;;
 esac
 if test "x${system_flags}" != "x"; then
   cmake_c_flags="${cmake_c_flags} ${system_flags}"