diff --git a/test/tbb/test_allocators.cpp b/test/tbb/test_allocators.cpp
index 78fd0cf565..7241cdbbf1 100644
--- a/test/tbb/test_allocators.cpp
+++ b/test/tbb/test_allocators.cpp
@@ -1,5 +1,5 @@
 /*
-    Copyright (c) 2005-2022 Intel Corporation
+    Copyright (c) 2005-2024 Intel Corporation
 
     Licensed under the Apache License, Version 2.0 (the "License");
     you may not use this file except in compliance with the License.
@@ -49,6 +49,7 @@ TEST_CASE("Test cache_aligned_allocate throws") {
     }
     REQUIRE_MESSAGE(address1, "cache_aligned_allocate unable to obtain 1024*1024 bytes");
 
+#if !EMSCRIPTEN
     bool exception_caught = false;
     try {
         // Try allocating more memory than left in the address space; should cause std::bad_alloc
@@ -60,7 +61,7 @@ TEST_CASE("Test cache_aligned_allocate throws") {
         exception_caught = true;
     }
     REQUIRE_MESSAGE(exception_caught, "cache_aligned_allocate did not throw bad_alloc");
-
+#endif
     try {
         cache_aligned_deallocate(address1);
     } catch (...) {
diff --git a/test/tbb/test_concurrent_unordered_map.cpp b/test/tbb/test_concurrent_unordered_map.cpp
index b676b455bf..f6db21e24f 100644
--- a/test/tbb/test_concurrent_unordered_map.cpp
+++ b/test/tbb/test_concurrent_unordered_map.cpp
@@ -1,5 +1,5 @@
 /*
-    Copyright (c) 2005-2023 Intel Corporation
+    Copyright (c) 2005-2024 Intel Corporation
 
     Licensed under the Apache License, Version 2.0 (the "License");
     you may not use this file except in compliance with the License.
@@ -103,6 +103,7 @@ void test_specific_types() {
                        (new int, new int);
 }
 
+#if !EMSCRIPTEN
 //! \brief \ref stress \ref error_guessing
 TEST_CASE("basic test for concurrent_unordered_map with degenerate hash") {
     test_basic<degenerate_map_type>();
@@ -264,3 +265,4 @@ TEST_CASE("reserve(0) issue regression test") {
     test_reserve_regression<oneapi::tbb::concurrent_unordered_map<int, int>>();
     test_reserve_regression<oneapi::tbb::concurrent_unordered_multimap<int, int>>();
 }
+#endif
diff --git a/test/tbb/test_concurrent_unordered_set.cpp b/test/tbb/test_concurrent_unordered_set.cpp
index 1b5195baab..f62513af37 100644
--- a/test/tbb/test_concurrent_unordered_set.cpp
+++ b/test/tbb/test_concurrent_unordered_set.cpp
@@ -1,5 +1,5 @@
 /*
-    Copyright (c) 2005-2023 Intel Corporation
+    Copyright (c) 2005-2024 Intel Corporation
 
     Licensed under the Apache License, Version 2.0 (the "License");
     you may not use this file except in compliance with the License.
@@ -84,6 +84,7 @@ void test_specific_types() {
                         std::false_type>(new int, new int);
 }
 
+#if !EMSCRIPTEN
 //! \brief \ref stress \ref error_guessing
 TEST_CASE("basic test for concurrent_unordered_set with degenerate hash") {
     test_basic<degenerate_set_type>();
@@ -235,3 +236,4 @@ TEST_CASE("reserve(0) issue regression test") {
     test_reserve_regression<oneapi::tbb::concurrent_unordered_set<int>>();
     test_reserve_regression<oneapi::tbb::concurrent_unordered_multiset<int>>();
 }
+#endif
diff --git a/test/tbb/test_task_arena.cpp b/test/tbb/test_task_arena.cpp
index fd930f1995..fb0c13eeca 100644
--- a/test/tbb/test_task_arena.cpp
+++ b/test/tbb/test_task_arena.cpp
@@ -1,5 +1,5 @@
 /*
-    Copyright (c) 2005-2023 Intel Corporation
+    Copyright (c) 2005-2024 Intel Corporation
 
     Licensed under the Apache License, Version 2.0 (the "License");
     you may not use this file except in compliance with the License.
@@ -1807,7 +1807,7 @@ void test_threads_sleep(int concurrency, int reserved_slots) {
 }
 
 //--------------------------------------------------//
-
+#if !EMSCRIPTEN
 // This test requires TBB in an uninitialized state
 //! \brief \ref requirement
 TEST_CASE("task_arena initialize soft limit ignoring affinity mask") {
@@ -1941,6 +1941,8 @@ TEST_CASE("Stress test with mixing functionality") {
     StressTestMixFunctionality();
 }
 
+// global_control::max_allowed_parallelism functionality is not covered by TCM
+#if !__TBB_TCM_TESTING_ENABLED
 //! \brief \ref stress
 TEST_CASE("Workers oversubscription") {
     std::size_t num_threads = utils::get_platform_max_threads();
@@ -1977,6 +1979,7 @@ TEST_CASE("Workers oversubscription") {
         );
     });
 }
+#endif
 
 #if TBB_USE_EXCEPTIONS
 //! The test for error in scheduling empty task_handle
@@ -2065,3 +2068,4 @@ TEST_CASE("worker threads occupy slots in correct range") {
 
     while (counter < 42) { utils::yield(); }
 }
+#endif
diff --git a/test/tbb/test_task_group.cpp b/test/tbb/test_task_group.cpp
index d39b4fc703..ef6bbcbd33 100644
--- a/test/tbb/test_task_group.cpp
+++ b/test/tbb/test_task_group.cpp
@@ -1,5 +1,5 @@
 /*
-    Copyright (c) 2005-2023 Intel Corporation
+    Copyright (c) 2005-2024 Intel Corporation
 
     Licensed under the Apache License, Version 2.0 (the "License");
     you may not use this file except in compliance with the License.
@@ -897,6 +897,7 @@ void run_deep_stealing(tbb::task_group& tg1, tbb::task_group& tg2, int num_tasks
     }
 }
 
+#if !EMSCRIPTEN
 // TODO: move to the conformance test
 //! Test for stack overflow avoidance mechanism.
 //! \brief \ref requirement
@@ -983,6 +984,7 @@ TEST_CASE("Test for stack overflow avoidance mechanism within arena") {
         CHECK(tasks_executed == 10000 + second_thread_executed);
     });
 }
+#endif
 
 //! Test checks that we can submit work to task_group asynchronously with waiting.
 //! \brief \ref regression