diff --git a/3rdparty/everest/CMakeLists.txt b/3rdparty/everest/CMakeLists.txt
index 782c0c563..c27a8e5ee 100644
--- a/3rdparty/everest/CMakeLists.txt
+++ b/3rdparty/everest/CMakeLists.txt
@@ -10,7 +10,7 @@ set(everest_src
 
 list(APPEND everest_inc ${CMAKE_CURRENT_SOURCE_DIR}/include ${CMAKE_CURRENT_SOURCE_DIR}/include/everest ${CMAKE_CURRENT_SOURCE_DIR}/include/everest/kremlib)
 
-execute_process(COMMAND ${PYTHON_EXECUTABLE} ${CMAKE_CURRENT_SOURCE_DIR}/../../scripts/config.py -f ${CMAKE_CURRENT_SOURCE_DIR}/../../include/mbedtls/config.h get MBEDTLS_ECDH_VARIANT_EVEREST_ENABLED RESULT_VARIABLE result)
+execute_process(COMMAND ${MBEDTLS_PYTHON_EXECUTABLE} ${CMAKE_CURRENT_SOURCE_DIR}/../../scripts/config.py -f ${CMAKE_CURRENT_SOURCE_DIR}/../../include/mbedtls/config.h get MBEDTLS_ECDH_VARIANT_EVEREST_ENABLED RESULT_VARIABLE result)
 
 if(${result} EQUAL 0)
 
diff --git a/CMakeLists.txt b/CMakeLists.txt
index c84194c63..1f675c1ee 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -51,18 +51,29 @@ set(CTR_DRBG_128_BIT_KEY_WARNING "${WARNING_BORDER}"
                          "${WARNING_BORDER}")
 
 # Python 3 is only needed here to check for configuration warnings.
-find_package(PythonInterp 3)
-if(PYTHONINTERP_FOUND)
+if(NOT CMAKE_VERSION VERSION_LESS 3.15.0)
+    set(Python3_FIND_STRATEGY LOCATION)
+    find_package(Python3 COMPONENTS Interpreter)
+    if(Python3_Interpreter_FOUND)
+        set(MBEDTLS_PYTHON_EXECUTABLE ${Python3_EXECUTABLE})
+    endif()
+else()
+    find_package(PythonInterp 3)
+    if(PYTHONINTERP_FOUND)
+        set(MBEDTLS_PYTHON_EXECUTABLE ${PYTHON_EXECUTABLE})
+    endif()
+endif()
+if(MBEDTLS_PYTHON_EXECUTABLE)
 
     # If 128-bit keys are configured for CTR_DRBG, display an appropriate warning
-    execute_process(COMMAND ${PYTHON_EXECUTABLE} ${CMAKE_CURRENT_SOURCE_DIR}/scripts/config.py -f ${CMAKE_CURRENT_SOURCE_DIR}/include/mbedtls/config.h get MBEDTLS_CTR_DRBG_USE_128_BIT_KEY
+    execute_process(COMMAND ${MBEDTLS_PYTHON_EXECUTABLE} ${CMAKE_CURRENT_SOURCE_DIR}/scripts/config.py -f ${CMAKE_CURRENT_SOURCE_DIR}/include/mbedtls/config.h get MBEDTLS_CTR_DRBG_USE_128_BIT_KEY
                         RESULT_VARIABLE result)
     if(${result} EQUAL 0)
         message(WARNING ${CTR_DRBG_128_BIT_KEY_WARNING})
     endif()
 
     # If NULL Entropy is configured, display an appropriate warning
-    execute_process(COMMAND ${PYTHON_EXECUTABLE} ${CMAKE_CURRENT_SOURCE_DIR}/scripts/config.py -f ${CMAKE_CURRENT_SOURCE_DIR}/include/mbedtls/config.h get MBEDTLS_TEST_NULL_ENTROPY
+    execute_process(COMMAND ${MBEDTLS_PYTHON_EXECUTABLE} ${CMAKE_CURRENT_SOURCE_DIR}/scripts/config.py -f ${CMAKE_CURRENT_SOURCE_DIR}/include/mbedtls/config.h get MBEDTLS_TEST_NULL_ENTROPY
                         RESULT_VARIABLE result)
     if(${result} EQUAL 0)
         message(WARNING ${NULL_ENTROPY_WARNING})
diff --git a/ChangeLog.d/use-find-python3-cmake.txt b/ChangeLog.d/use-find-python3-cmake.txt
new file mode 100644
index 000000000..36a5171ee
--- /dev/null
+++ b/ChangeLog.d/use-find-python3-cmake.txt
@@ -0,0 +1,2 @@
+Changes
+  * Use FindPython3 when cmake version >= 3.15.0
diff --git a/programs/psa/CMakeLists.txt b/programs/psa/CMakeLists.txt
index 201f987c7..4373cebc8 100644
--- a/programs/psa/CMakeLists.txt
+++ b/programs/psa/CMakeLists.txt
@@ -10,7 +10,7 @@ target_link_libraries(psa_constant_names mbedtls)
 
 add_custom_target(
     psa_constant_names_generated
-    COMMAND ${PYTHON_EXECUTABLE} scripts/generate_psa_constants.py ${CMAKE_CURRENT_BINARY_DIR}
+    COMMAND ${MBEDTLS_PYTHON_EXECUTABLE} scripts/generate_psa_constants.py ${CMAKE_CURRENT_BINARY_DIR}
     WORKING_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR}/../../
 )
 add_dependencies(psa_constant_names psa_constant_names_generated)
diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt
index 14a7b7e94..bd5ed8328 100644
--- a/tests/CMakeLists.txt
+++ b/tests/CMakeLists.txt
@@ -17,9 +17,8 @@ if(ENABLE_ZLIB_SUPPORT)
     set(libs ${libs} ${ZLIB_LIBRARIES})
 endif(ENABLE_ZLIB_SUPPORT)
 
-find_package(PythonInterp)
-if(NOT PYTHONINTERP_FOUND)
-    message(FATAL_ERROR "Cannot build test suites without Python 2 or 3")
+if(NOT MBEDTLS_PYTHON_EXECUTABLE)
+    message(FATAL_ERROR "Cannot build test suites without Python 3")
 endif()
 
 # Enable definition of various functions used throughout the testsuite
@@ -43,7 +42,7 @@ function(add_test_suite suite_name)
 
     add_custom_command(
         OUTPUT test_suite_${data_name}.c
-        COMMAND ${PYTHON_EXECUTABLE} ${CMAKE_CURRENT_SOURCE_DIR}/scripts/generate_test_code.py -f ${CMAKE_CURRENT_SOURCE_DIR}/suites/test_suite_${suite_name}.function -d ${CMAKE_CURRENT_SOURCE_DIR}/suites/test_suite_${data_name}.data -t ${CMAKE_CURRENT_SOURCE_DIR}/suites/main_test.function -p ${CMAKE_CURRENT_SOURCE_DIR}/suites/host_test.function -s ${CMAKE_CURRENT_SOURCE_DIR}/suites --helpers-file ${CMAKE_CURRENT_SOURCE_DIR}/suites/helpers.function -o .
+        COMMAND ${MBEDTLS_PYTHON_EXECUTABLE} ${CMAKE_CURRENT_SOURCE_DIR}/scripts/generate_test_code.py -f ${CMAKE_CURRENT_SOURCE_DIR}/suites/test_suite_${suite_name}.function -d ${CMAKE_CURRENT_SOURCE_DIR}/suites/test_suite_${data_name}.data -t ${CMAKE_CURRENT_SOURCE_DIR}/suites/main_test.function -p ${CMAKE_CURRENT_SOURCE_DIR}/suites/host_test.function -s ${CMAKE_CURRENT_SOURCE_DIR}/suites --helpers-file ${CMAKE_CURRENT_SOURCE_DIR}/suites/helpers.function -o .
         DEPENDS ${CMAKE_CURRENT_SOURCE_DIR}/scripts/generate_test_code.py mbedtls ${CMAKE_CURRENT_SOURCE_DIR}/suites/helpers.function ${CMAKE_CURRENT_SOURCE_DIR}/suites/main_test.function ${CMAKE_CURRENT_SOURCE_DIR}/suites/host_test.function ${CMAKE_CURRENT_SOURCE_DIR}/suites/test_suite_${suite_name}.function ${CMAKE_CURRENT_SOURCE_DIR}/suites/test_suite_${data_name}.data
     )