diff --git a/Misc/NEWS b/Misc/NEWS
index 142848bd9b1..263ba1d7722 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -132,6 +132,9 @@ C API
 Build
 -----
 
+- Issue #27434: The interpreter that runs the cross-build, found in PATH, must
+  now be of the same feature version (e.g. 3.6) as the source being built.
+
 - Issue #26930: Update Windows builds to use OpenSSL 1.0.2h.
 
 - Issue #23968: Rename the platform directory from plat-$(MACHDEP) to
diff --git a/configure b/configure
index f6a489259a1..fbde7f6f556 100755
--- a/configure
+++ b/configure
@@ -3002,7 +3002,7 @@ $as_echo_n "checking for python interpreter for cross build... " >&6; }
     if test -z "$PYTHON_FOR_BUILD"; then
         for interp in python$PACKAGE_VERSION python3 python; do
 	    which $interp >/dev/null 2>&1 || continue
-	    if $interp -c 'import sys;sys.exit(not sys.version_info[:2] >= (3,3))'; then
+	    if $interp -c "import sys;sys.exit(not '.'.join(str(n) for n in sys.version_info[:2]) == '$PACKAGE_VERSION')"; then
 	        break
 	    fi
             interp=
diff --git a/configure.ac b/configure.ac
index 60e8089d678..9b65ec16a4e 100644
--- a/configure.ac
+++ b/configure.ac
@@ -62,7 +62,7 @@ if test "$cross_compiling" = yes; then
     if test -z "$PYTHON_FOR_BUILD"; then
         for interp in python$PACKAGE_VERSION python3 python; do
 	    which $interp >/dev/null 2>&1 || continue
-	    if $interp -c 'import sys;sys.exit(not sys.version_info@<:@:2@:>@ >= (3,3))'; then
+	    if $interp -c "import sys;sys.exit(not '.'.join(str(n) for n in sys.version_info@<:@:2@:>@) == '$PACKAGE_VERSION')"; then
 	        break
 	    fi
             interp=