diff --git a/NEWS b/NEWS
index 3eb9779fde9..66896a7328f 100644
--- a/NEWS
+++ b/NEWS
@@ -55,6 +55,8 @@ PHP                                                                        NEWS
   . Fixed floating point exception bug with gmp_pow when using
     large exposant values. (David Carlier).
   . Fixed bug GH-16411 (gmp_export() can cause overflow). (cmb)
+  . Fixed bug GH-16501 (gmp_random_bits() can cause overflow).
+    (David Carlier)
 
 - MBstring:
   . Fixed bug GH-16361 (mb_substr overflow on start/length arguments).
diff --git a/ext/gmp/gmp.c b/ext/gmp/gmp.c
index f3cb4a6ce10..14ce57aa49b 100644
--- a/ext/gmp/gmp.c
+++ b/ext/gmp/gmp.c
@@ -1821,15 +1821,21 @@ ZEND_FUNCTION(gmp_random_bits)
 		RETURN_THROWS();
 	}
 
-	if (bits <= 0) {
-		zend_argument_value_error(1, "must be greater than or equal to 1");
+#if SIZEOF_SIZE_T == 4
+	const zend_long maxbits = ULONG_MAX / GMP_NUMB_BITS;
+#else
+	const zend_long maxbits = INT_MAX;
+#endif
+
+	if (bits <= 0 || bits > maxbits) {
+		zend_argument_value_error(1, "must be between 1 and " ZEND_LONG_FMT, maxbits);
 		RETURN_THROWS();
 	}
 
 	INIT_GMP_RETVAL(gmpnum_result);
 	gmp_init_random();
 
-	mpz_urandomb(gmpnum_result, GMPG(rand_state), bits);
+	mpz_urandomb(gmpnum_result, GMPG(rand_state), (mp_bitcnt_t)bits);
 }
 /* }}} */
 
diff --git a/ext/gmp/tests/gh16501.phpt b/ext/gmp/tests/gh16501.phpt
new file mode 100644
index 00000000000..325be85d191
--- /dev/null
+++ b/ext/gmp/tests/gh16501.phpt
@@ -0,0 +1,14 @@
+--TEST--
+GH-16501 (gmp_random_bits overflow)
+--EXTENSIONS--
+gmp
+--FILE--
+<?php
+try {
+	gmp_random_bits(PHP_INT_MAX);
+} catch (\ValueError $e) {
+	echo $e->getMessage();
+}
+?>
+--EXPECTF--
+gmp_random_bits(): Argument #1 ($bits) must be between 1 and %d
diff --git a/ext/gmp/tests/gmp_random_bits.phpt b/ext/gmp/tests/gmp_random_bits.phpt
index 3dbfc097d28..4e7f3379838 100644
--- a/ext/gmp/tests/gmp_random_bits.phpt
+++ b/ext/gmp/tests/gmp_random_bits.phpt
@@ -40,7 +40,7 @@ while (1) {
 
 echo "Done\n";
 ?>
---EXPECT--
-gmp_random_bits(): Argument #1 ($bits) must be greater than or equal to 1
-gmp_random_bits(): Argument #1 ($bits) must be greater than or equal to 1
+--EXPECTF--
+gmp_random_bits(): Argument #1 ($bits) must be between 1 and %d
+gmp_random_bits(): Argument #1 ($bits) must be between 1 and %d
 Done