diff --git a/include/pybind11/detail/common.h b/include/pybind11/detail/common.h
index 3faf3ea32..0b4e30c18 100644
--- a/include/pybind11/detail/common.h
+++ b/include/pybind11/detail/common.h
@@ -56,6 +56,9 @@
 #  elif __INTEL_COMPILER < 1900 && defined(PYBIND11_CPP14)
 #    error pybind11 supports only C++11 with Intel C++ compiler v18. Use v19 or newer for C++14.
 #  endif
+/* The following pragma cannot be pop'ed:
+   https://community.intel.com/t5/Intel-C-Compiler/Inline-and-no-inline-warning/td-p/1216764 */
+#  pragma warning disable 2196 // warning #2196: routine is both "inline" and "noinline"
 #elif defined(__clang__) && !defined(__apple_build_version__)
 #  if __clang_major__ < 3 || (__clang_major__ == 3 && __clang_minor__ < 3)
 #    error pybind11 requires clang 3.3 or newer
diff --git a/include/pybind11/pybind11.h b/include/pybind11/pybind11.h
index e2cbb5449..b14aff58a 100644
--- a/include/pybind11/pybind11.h
+++ b/include/pybind11/pybind11.h
@@ -10,16 +10,12 @@
 
 #pragma once
 
-#if defined(__INTEL_COMPILER)
-#  pragma warning push
-#  pragma warning disable 878   // incompatible exception specifications
-#  pragma warning disable 2196  // warning #2196: routine is both "inline" and "noinline"
-#elif defined(_MSC_VER)
+#if defined(_MSC_VER) && !defined(__INTEL_COMPILER)
 #  pragma warning(push)
 #  pragma warning(disable: 4100) // warning C4100: Unreferenced formal parameter
 #  pragma warning(disable: 4127) // warning C4127: Conditional expression is constant
 #  pragma warning(disable: 4505) // warning C4505: 'PySlice_GetIndicesEx': unreferenced local function has been removed (PyPy only)
-#elif defined(__GNUG__) && !defined(__clang__)
+#elif defined(__GNUG__) && !defined(__clang__) && !defined(__INTEL_COMPILER)
 #  pragma GCC diagnostic push
 #  pragma GCC diagnostic ignored "-Wunused-but-set-parameter"
 #  pragma GCC diagnostic ignored "-Wattributes"
diff --git a/tests/test_constants_and_functions.cpp b/tests/test_constants_and_functions.cpp
index e7f018540..c0554503f 100644
--- a/tests/test_constants_and_functions.cpp
+++ b/tests/test_constants_and_functions.cpp
@@ -133,7 +133,14 @@ TEST_SUBMODULE(constants_and_functions, m) {
         ;
     m.def("f1", f1);
     m.def("f2", f2);
+#if defined(__INTEL_COMPILER)
+#    pragma warning push
+#    pragma warning disable 878 // incompatible exception specifications
+#endif
     m.def("f3", f3);
+#if defined(__INTEL_COMPILER)
+#    pragma warning pop
+#endif
     m.def("f4", f4);
 
     // test_function_record_leaks