diff --git a/src/mistune/renderers/markdown.py b/src/mistune/renderers/markdown.py
index 1626980..b49081a 100644
--- a/src/mistune/renderers/markdown.py
+++ b/src/mistune/renderers/markdown.py
@@ -114,7 +114,8 @@ def block_code(self, token: Dict[str, Any], state: BlockState) -> str:
         return marker2 + info + "\n" + code + marker2 + "\n\n"
 
     def block_quote(self, token: Dict[str, Any], state: BlockState) -> str:
-        text = indent(self.render_children(token, state), '> ')
+        text = indent(self.render_children(token, state), '> ', lambda _: True)
+        text = text.rstrip("> \n")
         return text + '\n\n'
 
     def block_html(self, token: Dict[str, Any], state: BlockState) -> str:
diff --git a/tests/fixtures/renderer_markdown.txt b/tests/fixtures/renderer_markdown.txt
index 1440875..fd618f9 100644
--- a/tests/fixtures/renderer_markdown.txt
+++ b/tests/fixtures/renderer_markdown.txt
@@ -228,6 +228,18 @@ hello
 > quote
 ````````````````````````````````
 
+> quote
+
+> quote
+> 
+> continuation
+.
+> quote
+
+> quote
+> 
+> continuation
+
 ## list
 
 ```````````````````````````````` example