diff --git a/.github/workflows/linux_simd.yml b/.github/workflows/linux_simd.yml
index 4cd87ab37dd4..a9f065e25cc0 100644
--- a/.github/workflows/linux_simd.yml
+++ b/.github/workflows/linux_simd.yml
@@ -212,7 +212,7 @@ jobs:
         python -m pip install pytest pytest-xdist hypothesis typing_extensions
 
     - name: Build
-      run: CC=gcc-13 CXX=g++-13 spin build -- -Dallow-noblas=true -Dcpu-baseline=avx512_skx -Dtest-simd='BASELINE,AVX512_KNL,AVX512_KNM,AVX512_SKX,AVX512_CLX,AVX512_CNL,AVX512_ICL,AVX512_SPR'
+      run: CC=gcc-13 CXX=g++-13 spin build -- -Denable-openmp=true -Dallow-noblas=true -Dcpu-baseline=avx512_skx -Dtest-simd='BASELINE,AVX512_KNL,AVX512_KNM,AVX512_SKX,AVX512_CLX,AVX512_CNL,AVX512_ICL,AVX512_SPR'
 
     - name: Meson Log
       if: always()
@@ -263,7 +263,7 @@ jobs:
         python -m pip install pytest pytest-xdist hypothesis typing_extensions
 
     - name: Build
-      run: CC=gcc-13 CXX=g++-13 spin build -- -Dallow-noblas=true -Dcpu-baseline=avx512_spr
+      run: CC=gcc-13 CXX=g++-13 spin build -- -Denable-openmp=true -Dallow-noblas=true -Dcpu-baseline=avx512_spr
 
     - name: Meson Log
       if: always()
diff --git a/doc/release/upcoming_changes/28619.highlight.rst b/doc/release/upcoming_changes/28619.highlight.rst
new file mode 100644
index 000000000000..6c296b92899e
--- /dev/null
+++ b/doc/release/upcoming_changes/28619.highlight.rst
@@ -0,0 +1,6 @@
+Building NumPy with OpenMP Parallelization
+-------------------------------------------
+NumPy now supports OpenMP parallel processing capabilities when built with the
+``-Denable_openmp=true`` Meson build flag. This feature is disabled by default.
+When enabled, ``np.sort`` and ``np.argsort`` functions can utilize OpenMP for
+parallel thread execution, improving performance for these operations.
diff --git a/doc/release/upcoming_changes/28619.performance.rst b/doc/release/upcoming_changes/28619.performance.rst
new file mode 100644
index 000000000000..904decbe0ba6
--- /dev/null
+++ b/doc/release/upcoming_changes/28619.performance.rst
@@ -0,0 +1,7 @@
+Performance improvements to ``np.sort`` and ``np.argsort``
+----------------------------------------------------------
+``np.sort`` and ``np.argsort`` functions now can leverage OpenMP for parallel
+thread execution, resulting in up to 3.5x speedups on x86 architectures with
+AVX2 or AVX-512 instructions. This opt-in feature requires NumPy to be built
+with the -Denable_openmp Meson flag. Users can control the number of threads
+used by setting the OMP_NUM_THREADS environment variable.
diff --git a/meson.options b/meson.options
index 1be05d324756..b09992fe9b91 100644
--- a/meson.options
+++ b/meson.options
@@ -22,6 +22,8 @@ option('disable-intel-sort', type: 'boolean', value: false,
         description: 'Disables SIMD-optimized operations related to Intel x86-simd-sort')
 option('disable-threading', type: 'boolean', value: false,
         description: 'Disable threading support (see `NPY_ALLOW_THREADS` docs)')
+option('enable-openmp', type: 'boolean', value: false,
+        description: 'Enable building NumPy with openmp support')
 option('disable-optimization', type: 'boolean', value: false,
         description: 'Disable CPU optimized code (dispatch,simd,unroll...)')
 option('cpu-baseline', type: 'string', value: 'min',
diff --git a/numpy/_core/meson.build b/numpy/_core/meson.build
index 3bffed752474..a4d2050122c6 100644
--- a/numpy/_core/meson.build
+++ b/numpy/_core/meson.build
@@ -128,6 +128,21 @@ if use_intel_sort and not fs.exists('src/npysort/x86-simd-sort/README.md')
   error('Missing the `x86-simd-sort` git submodule! Run `git submodule update --init` to fix this.')
 endif
 
+# openMP related settings:
+if get_option('disable-threading') and get_option('enable-openmp')
+  error('Build options `disable-threading` and `enable-openmp` are conflicting. Please set at most one to true.')
+endif
+
+use_openmp = get_option('enable-openmp') and not get_option('disable-threading')
+
+# Setup openmp flags for x86-simd-sort:
+omp = []
+omp_dep = []
+if use_intel_sort and use_openmp
+  omp = dependency('openmp', required : true)
+  omp_dep = declare_dependency(dependencies: omp, compile_args: ['-DXSS_USE_OPENMP'])
+endif
+
 if not fs.exists('src/common/pythoncapi-compat')
   error('Missing the `pythoncapi-compat` git submodule! ' +
         'Run `git submodule update --init` to fix this.')
@@ -867,12 +882,15 @@ foreach gen_mtargets : [
     ] : []
   ],
 ]
+
+
+
   mtargets = mod_features.multi_targets(
     gen_mtargets[0], multiarray_gen_headers + gen_mtargets[1],
     dispatch: gen_mtargets[2],
     # baseline: CPU_BASELINE, it doesn't provide baseline fallback
     prefix: 'NPY_',
-    dependencies: [py_dep, np_core_dep],
+    dependencies: [py_dep, np_core_dep, omp_dep],
     c_args: c_args_common + max_opt,
     cpp_args: cpp_args_common + max_opt,
     include_directories: [
@@ -1286,7 +1304,7 @@ py.extension_module('_multiarray_umath',
     'src/umath',
     'src/highway'
   ],
-  dependencies: [blas_dep],
+  dependencies: [blas_dep, omp],
   link_with: [
     npymath_lib,
     unique_hash_so,
diff --git a/numpy/_core/src/npysort/x86-simd-sort b/numpy/_core/src/npysort/x86-simd-sort
index 9a1b616d5cd4..c306ac581a59 160000
--- a/numpy/_core/src/npysort/x86-simd-sort
+++ b/numpy/_core/src/npysort/x86-simd-sort
@@ -1 +1 @@
-Subproject commit 9a1b616d5cd4eaf49f7664fb86ccc1d18bad2b8d
+Subproject commit c306ac581a59f89585d778254c4ed7197e64ba2d
diff --git a/numpy/_core/tests/test_multiarray.py b/numpy/_core/tests/test_multiarray.py
index 0a62cb6945f0..d58471247682 100644
--- a/numpy/_core/tests/test_multiarray.py
+++ b/numpy/_core/tests/test_multiarray.py
@@ -10292,6 +10292,21 @@ def test_argsort_int(N, dtype):
     arr[N - 1] = maxv
     assert_arg_sorted(arr, np.argsort(arr, kind='quick'))
 
+# Test large arrays that leverage openMP implementations from x86-simd-sort:
+@pytest.mark.parametrize("dtype", [np.float16, np.float32, np.float64])
+def test_sort_largearrays(dtype):
+    N = 1000000
+    rnd = np.random.RandomState(1100710816)
+    arr = -0.5 + rnd.random(N).astype(dtype)
+    assert_equal(np.sort(arr, kind='quick'), np.sort(arr, kind='heap'))
+
+# Test large arrays that leverage openMP implementations from x86-simd-sort:
+@pytest.mark.parametrize("dtype", [np.float32, np.float64])
+def test_argsort_largearrays(dtype):
+    N = 1000000
+    rnd = np.random.RandomState(1100710816)
+    arr = -0.5 + rnd.random(N).astype(dtype)
+    assert_arg_sorted(arr, np.argsort(arr, kind='quick'))
 
 @pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
 def test_gh_22683():