diff --git a/Help/release/dev/ExternalProject-add-lzma.rst b/Help/release/dev/ExternalProject-add-lzma.rst
new file mode 100644
index 000000000..cb398efdd
--- /dev/null
+++ b/Help/release/dev/ExternalProject-add-lzma.rst
@@ -0,0 +1,5 @@
+ExternalProject-add-lzma
+------------------------
+
+* The :module:`ExternalProject` module learned to support lzma-compressed
+  source tarballs with ``.7z``, ``.tar.xz``, and ``.txz`` extensions.
diff --git a/Modules/ExternalProject.cmake b/Modules/ExternalProject.cmake
index 0d35cca1e..dbce9f4ca 100644
--- a/Modules/ExternalProject.cmake
+++ b/Modules/ExternalProject.cmake
@@ -737,7 +737,7 @@ endfunction()
 function(_ep_write_extractfile_script script_filename name filename directory)
   set(args "")
 
-  if(filename MATCHES "(\\.|=)(bz2|tar\\.gz|tgz|zip)$")
+  if(filename MATCHES "(\\.|=)(7z|tar\\.bz2|tar\\.gz|tar\\.xz|tbz2|tgz|txz|zip)$")
     set(args xfz)
   endif()
 
@@ -746,7 +746,7 @@ function(_ep_write_extractfile_script script_filename name filename directory)
   endif()
 
   if(args STREQUAL "")
-    message(SEND_ERROR "error: do not know how to extract '${filename}' -- known types are .bz2, .tar, .tar.gz, .tgz and .zip")
+    message(SEND_ERROR "error: do not know how to extract '${filename}' -- known types are .7z, .tar, .tar.bz2, .tar.gz, .tar.xz, .tbz2, .tgz, .txz and .zip")
     return()
   endif()
 
@@ -1540,11 +1540,11 @@ function(_ep_add_download_command name)
         if("x${fname}" STREQUAL "x")
           string(REGEX MATCH "[^/\\?]*$" fname "${url}")
         endif()
-        if(NOT "${fname}" MATCHES "(\\.|=)(bz2|tar|tgz|tar\\.gz|zip)$")
-          string(REGEX MATCH "([^/\\?]+(\\.|=)(bz2|tar|tgz|tar\\.gz|zip))/.*$" match_result "${url}")
+        if(NOT "${fname}" MATCHES "(\\.|=)(7z|tar|tar\\.bz2|tar\\.gz|tar\\.xz|tbz2|tgz|txz|zip)$")
+          string(REGEX MATCH "([^/\\?]+(\\.|=)(7z|tar|tar\\.bz2|tar\\.gz|tar\\.xz|tbz2|tgz|txz|zip))/.*$" match_result "${url}")
           set(fname "${CMAKE_MATCH_1}")
         endif()
-        if(NOT "${fname}" MATCHES "(\\.|=)(bz2|tar|tgz|tar\\.gz|zip)$")
+        if(NOT "${fname}" MATCHES "(\\.|=)(7z|tar|tar\\.bz2|tar\\.gz|tar\\.xz|tbz2|tgz|txz|zip)$")
           message(FATAL_ERROR "Could not extract tarball filename from url:\n  ${url}")
         endif()
         string(REPLACE ";" "-" fname "${fname}")