diff --git a/jsonschema/_format.py b/jsonschema/_format.py
index 5efda86e6..cd057f0f8 100644
--- a/jsonschema/_format.py
+++ b/jsonschema/_format.py
@@ -488,8 +488,11 @@ def is_relative_json_pointer(instance: object) -> bool:
         non_negative_integer, rest = [], ""
         for i, character in enumerate(instance):
             if character.isdigit():
-                # digits with a leading "0" are not allowed
-                if i > 0 and int(instance[i - 1]) == 0:
+                # a leading "0" is not allowed: "0" by itself is valid, but a
+                # multi-digit integer may not start with "0" (e.g. "01"). Only
+                # the single accumulated "0" followed by another digit is a
+                # leading zero -- "100"/"205" are fine.
+                if non_negative_integer == ["0"]:
                     return False
 
                 non_negative_integer.append(character)
diff --git a/jsonschema/tests/test_format.py b/jsonschema/tests/test_format.py
index d829f9848..6d4183006 100644
--- a/jsonschema/tests/test_format.py
+++ b/jsonschema/tests/test_format.py
@@ -80,6 +80,25 @@ def test_format_checkers_come_with_defaults(self):
         with self.assertRaises(FormatError):
             checker.check(instance="not-an-ipv4", format="ipv4")
 
+    def test_relative_json_pointer_allows_multidigit_integers(self):
+        checker = FormatChecker()
+        if "relative-json-pointer" not in checker.checkers:
+            self.skipTest("jsonpointer is not available")
+
+        # Only a *leading* zero is disallowed; a multi-digit integer with an
+        # internal or trailing zero is valid.
+        valids = ("0", "1", "120", "100", "205", "1000", "100/foo", "100#")
+        for valid in valids:
+            self.assertTrue(
+                checker.conforms(valid, "relative-json-pointer"),
+                msg=f"{valid!r} should be a valid relative-json-pointer",
+            )
+        for invalid in ("01", "00", "007", "01/a", "01#"):
+            self.assertFalse(
+                checker.conforms(invalid, "relative-json-pointer"),
+                msg=f"{invalid!r} should not be a valid relative-json-pointer",
+            )
+
     def test_repr(self):
         checker = FormatChecker(formats=())
         checker.checks("foo")(lambda thing: True)  # pragma: no cover