diff --git a/sysdeps/x86_64/Makefile b/sysdeps/x86_64/Makefile
index 374bca80d0..836e03a224 100644
--- a/sysdeps/x86_64/Makefile
+++ b/sysdeps/x86_64/Makefile
@@ -186,9 +186,11 @@ endif
 ifeq (yes,$(have-z-mark-plt))
 tests += \
   tst-plt-rewrite1 \
+  tst-plt-rewrite2 \
 # tests
 modules-names += \
   tst-plt-rewritemod1 \
+  tst-plt-rewritemod2 \
 # modules-names
 
 tst-plt-rewrite1-no-pie = yes
@@ -200,6 +202,12 @@ $(objpfx)tst-plt-rewrite1.out: /dev/null $(objpfx)tst-plt-rewrite1
 	$(tst-plt-rewrite1-ENV) $(make-test-out) > $@ 2>&1; \
 	grep -q -E "changing 'bar' PLT entry in .*/elf/tst-plt-rewritemod1.so' to direct branch" $@; \
 	$(evaluate-test)
+
+tst-plt-rewrite2-no-pie = yes
+LDFLAGS-tst-plt-rewrite2 = -Wl,-z,now
+LDFLAGS-tst-plt-rewritemod2.so = -Wl,-z,now,-z,undefs
+tst-plt-rewrite2-ENV = GLIBC_TUNABLES=glibc.cpu.plt_rewrite=2
+$(objpfx)tst-plt-rewrite2: $(objpfx)tst-plt-rewritemod2.so
 endif
 
 endif # $(subdir) == elf
diff --git a/sysdeps/x86_64/dl-machine.h b/sysdeps/x86_64/dl-machine.h
index ca290ef082..2d2ce503a5 100644
--- a/sysdeps/x86_64/dl-machine.h
+++ b/sysdeps/x86_64/dl-machine.h
@@ -607,8 +607,9 @@ x86_64_rewrite_plt (struct link_map *map, ElfW(Addr) plt_rewrite)
 	/* Skip ENDBR64 if IBT isn't enabled.  */
 	if (!ibt_enabled_p)
 	  branch_start = ALIGN_DOWN (branch_start, pltent);
-	/* Get the displacement from the branch target.  */
-	ElfW(Addr) disp = value - branch_start - JMP32_INSN_SIZE;
+	/* Get the displacement from the branch target.  NB: We must use
+	   64-bit integer on x32 to avoid overflow.  */
+	uint64_t disp = (uint64_t) value - branch_start - JMP32_INSN_SIZE;
 	ElfW(Addr) plt_end;
 	ElfW(Addr) pad;
 
diff --git a/sysdeps/x86_64/tst-plt-rewrite2.c b/sysdeps/x86_64/tst-plt-rewrite2.c
new file mode 100644
index 0000000000..8427df5605
--- /dev/null
+++ b/sysdeps/x86_64/tst-plt-rewrite2.c
@@ -0,0 +1,46 @@
+/* Test PLT rewrite with 32-bit displacement overflow.
+   Copyright (C) 2024 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <https://www.gnu.org/licenses/>.  */
+
+#include <support/check.h>
+
+extern int (*func_p) (void);
+extern void foo (void);
+
+int
+func (void)
+{
+  return 0xbadbeef;
+}
+
+void
+bar (void)
+{
+  TEST_VERIFY (func_p == &func);
+  TEST_VERIFY (func_p () == 0xbadbeef);
+}
+
+static int
+do_test (void)
+{
+  func_p = &func;
+  foo ();
+  bar ();
+  return 0;
+}
+
+#include <support/test-driver.c>
diff --git a/sysdeps/x86_64/tst-plt-rewritemod2.c b/sysdeps/x86_64/tst-plt-rewritemod2.c
new file mode 100644
index 0000000000..4a86d736b5
--- /dev/null
+++ b/sysdeps/x86_64/tst-plt-rewritemod2.c
@@ -0,0 +1,32 @@
+/* Check PLT rewrite with 32-bit displacement overflow.
+   Copyright (C) 2024 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <https://www.gnu.org/licenses/>.  */
+
+/* foo calls func with indirect branch via PLT.  PLT rewrite shouldn't
+   change it to direct branch if func is too far way.  */
+
+#include <support/check.h>
+
+int (*func_p) (void);
+extern int func (void);
+
+void
+foo (void)
+{
+  TEST_VERIFY (func () == 0xbadbeef);
+  TEST_VERIFY (func_p () == 0xbadbeef);
+}