diff --git a/fsspec/implementations/dirfs.py b/fsspec/implementations/dirfs.py
index 04f7479ad..a42ca78d0 100644
--- a/fsspec/implementations/dirfs.py
+++ b/fsspec/implementations/dirfs.py
@@ -64,9 +64,13 @@ def _relpath(self, path):
         if isinstance(path, str):
             if not self.path:
                 return path
-            if path == self.path:
+            # We need to account for S3FileSystem returning paths that do not
+            # start with a '/'
+            if path == self.path or (self.path.startswith(self.fs.sep) and path == self.path[1:]):
                 return ""
             prefix = self.path + self.fs.sep
+            if self.path.startswith(self.fs.sep) and not path.startswith(self.fs.sep):
+                prefix = prefix[1:]
             assert path.startswith(prefix)
             return path[len(prefix) :]
         return [self._relpath(_path) for _path in path]
diff --git a/fsspec/implementations/tests/test_dirfs.py b/fsspec/implementations/tests/test_dirfs.py
index c04ba66a7..990ab11de 100644
--- a/fsspec/implementations/tests/test_dirfs.py
+++ b/fsspec/implementations/tests/test_dirfs.py
@@ -82,6 +82,8 @@ def test_dirfs(fs, asyncfs):
         ("", "foo", "foo"),
         ("root", "", "root"),
         ("root", "foo", "root/foo"),
+        ("/root", "", "/root"),
+        ("/root", "foo", "/root/foo"),
     ],
 )
 def test_path(fs, root, rel, full):
@@ -90,6 +92,18 @@ def test_path(fs, root, rel, full):
     assert dirfs._relpath(full) == rel
 
 
+@pytest.mark.parametrize(
+    "root, rel, full",
+    [
+        ("/root", "foo", "root/foo"),
+        ("/root", "", "root"),
+    ],
+)
+def test_path_no_leading_slash(fs, root, rel, full):
+    dirfs = DirFileSystem(root, fs)
+    assert dirfs._relpath(full) == rel
+
+
 def test_sep(mocker, dirfs):
     sep = mocker.Mock()
     dirfs.fs.sep = sep