diff --git a/build/pkgs/configure/checksums.ini b/build/pkgs/configure/checksums.ini
index 725d4af02ac..1680e98b873 100644
--- a/build/pkgs/configure/checksums.ini
+++ b/build/pkgs/configure/checksums.ini
@@ -1,3 +1,3 @@
 tarball=configure-VERSION.tar.gz
-sha1=605eb62e991cc1216d9590f2de779b00c4b7c98a
-sha256=b1cc158f4a15f8d0aebf9253b706a1b0797561ed27f30cce725ec5e216dd004e
+sha1=cd591331e799bec71cacd6130f8bbfbfe8bec061
+sha256=7d915cc7ac39f43da4f2c9da68de0ccf29b0c142f4f6bba12529967e294f646c
diff --git a/build/pkgs/configure/package-version.txt b/build/pkgs/configure/package-version.txt
index 29c851ebc04..1c29d4dd137 100644
--- a/build/pkgs/configure/package-version.txt
+++ b/build/pkgs/configure/package-version.txt
@@ -1 +1 @@
-266b7569daa9d9be93e06f83e5d1eda01536f0bd
+a3e5895b20f7c558ae0deede673a72cf84c814d3
diff --git a/build/pkgs/gmp/spkg-install.in b/build/pkgs/gmp/spkg-install.in
index baacc5132b1..9e6227eb01d 100644
--- a/build/pkgs/gmp/spkg-install.in
+++ b/build/pkgs/gmp/spkg-install.in
@@ -98,10 +98,16 @@ if [ "$SAGE_FAT_BINARY" = "yes" ]; then
     esac
 fi
 
+# Make configure tests use our own libstdc++ if it is available
+# See https://github.com/sagemath/sage/issues/38085
+CXXFLAGS_CONFIGURE="-Wl,-rpath -Wl,$SAGE_LOCAL/lib"
 
 # Pre-configure GMP to get the settings it would use if CFLAGS were empty:
 echo "Checking what CFLAGS GMP would use if they were empty..."
-(unset CFLAGS CPPFLAGS CXXFLAGS && ./configure $GMP_CONFIGURE) &>configure-empty.log
+(
+    unset CFLAGS CPPFLAGS CXXFLAGS &&
+    CXXFLAGS=$CXXFLAGS_CONFIGURE ./configure $GMP_CONFIGURE
+) &>configure-empty.log
 if [ $? -ne 0 ]; then
     # Output the log of the failed configure run
     cat configure-empty.log
@@ -163,7 +169,7 @@ echo "You can set GMP_CONFIGURE to pass additional parameters."
 # Clear the cache of the previous configure run
 find . -name config.cache -exec rm -f {} \;
 
-./configure --prefix="$SAGE_LOCAL" --libdir="$SAGE_LOCAL/lib" $GMP_CONFIGURE
+CXXFLAGS=$CXXFLAGS_CONFIGURE ./configure --prefix="$SAGE_LOCAL" --libdir="$SAGE_LOCAL/lib" $GMP_CONFIGURE
 if [ $? -ne 0 ]; then
     echo >&2 "Error configuring GMP. (See above for the options passed to it.)"
     exit 1