diff --git a/Help/release/dev/externalproject-archive-types.rst b/Help/release/dev/externalproject-archive-types.rst
new file mode 100644
index 0000000000..a748a38236
--- /dev/null
+++ b/Help/release/dev/externalproject-archive-types.rst
@@ -0,0 +1,6 @@
+externalproject-archive-types
+-----------------------------
+
+* The :module:`ExternalProject` module no longer checks the ``URL`` archive
+  file extension.  Any archive type that :option:`cmake -E tar <cmake-E tar>`
+  can extract is now allowed.
diff --git a/Modules/ExternalProject.cmake b/Modules/ExternalProject.cmake
index 37bd39cae3..61e2ea5656 100644
--- a/Modules/ExternalProject.cmake
+++ b/Modules/ExternalProject.cmake
@@ -301,6 +301,10 @@ URL
 .. versionadded:: 3.1
   Added support for `tbz2`, `.tar.xz`, `.txz`, and `.7z` extensions.
 
+.. versionadded:: 4.1
+  All archive types that :option:`cmake -E tar <cmake-E tar>` can extract
+  are supported regardless of file extension.
+
 Git
 ~~~
 
diff --git a/Modules/ExternalProject/shared_internal_commands.cmake b/Modules/ExternalProject/shared_internal_commands.cmake
index ac5d2bddc3..cb7b772225 100644
--- a/Modules/ExternalProject/shared_internal_commands.cmake
+++ b/Modules/ExternalProject/shared_internal_commands.cmake
@@ -701,23 +701,8 @@ function(_ep_write_extractfile_script
   directory
   options
 )
-  set(args "")
-
-  if(filename MATCHES
-    "(\\.|=)(7z|tar\\.bz2|tar\\.gz|tar\\.xz|tbz2|tgz|txz|zip)$")
-    set(args xfz)
-  endif()
-
-  if(filename MATCHES "(\\.|=)tar$")
-    set(args xf)
-  endif()
-
-  if(args STREQUAL "")
-    message(FATAL_ERROR
-      "Do not know how to extract '${filename}' -- known types are: "
-      ".7z, .tar, .tar.bz2, .tar.gz, .tar.xz, .tbz2, .tgz, .txz and .zip"
-    )
-  endif()
+  # cmake -E tar auto detects the type of archive being extracted
+  set(args "xf")
 
   configure_file(
     "${CMAKE_CURRENT_FUNCTION_LIST_DIR}/extractfile.cmake.in"
diff --git a/Tests/ExternalProjectLocal/CMakeLists.txt b/Tests/ExternalProjectLocal/CMakeLists.txt
index c956fe4d01..8f753bcd50 100644
--- a/Tests/ExternalProjectLocal/CMakeLists.txt
+++ b/Tests/ExternalProjectLocal/CMakeLists.txt
@@ -142,7 +142,7 @@ set_property(TARGET ${proj} PROPERTY FOLDER "Local/TGZ")
 #  this more complete, we should add a diff between this and the TGZ tree since
 #  that one does build.
 #
-set(extra_cmp_exts tar.bz2 tar.xz zip)
+set(extra_cmp_exts tar.bz2 tar.xz tar.zst zip)
 foreach(ext IN LISTS extra_cmp_exts)
   string(TOUPPER "${ext}" name)
 
diff --git a/Tests/ExternalProjectLocal/Step1.tar.zst b/Tests/ExternalProjectLocal/Step1.tar.zst
new file mode 100644
index 0000000000..3731108d23
Binary files /dev/null and b/Tests/ExternalProjectLocal/Step1.tar.zst differ
diff --git a/Tests/ExternalProjectLocal/Step1NoDir.tar.zst b/Tests/ExternalProjectLocal/Step1NoDir.tar.zst
new file mode 100644
index 0000000000..f453b750ea
Binary files /dev/null and b/Tests/ExternalProjectLocal/Step1NoDir.tar.zst differ