diff --git a/httpcore/_async/http2.py b/httpcore/_async/http2.py
index 025daf02e..73705419b 100644
--- a/httpcore/_async/http2.py
+++ b/httpcore/_async/http2.py
@@ -306,6 +306,7 @@ async def aclose(self) -> None:
         # Note that this method unilaterally closes the connection, and does
         # not have any kind of locking in place around it.
         # For task-safe/thread-safe operations call into 'attempt_close' instead.
+        self._h2_state.close_connection()
         self._state = HTTPConnectionState.CLOSED
         await self._network_stream.aclose()
 
diff --git a/httpcore/_sync/http2.py b/httpcore/_sync/http2.py
index 97ac0ecc0..929db8512 100644
--- a/httpcore/_sync/http2.py
+++ b/httpcore/_sync/http2.py
@@ -306,6 +306,7 @@ def close(self) -> None:
         # Note that this method unilaterally closes the connection, and does
         # not have any kind of locking in place around it.
         # For task-safe/thread-safe operations call into 'attempt_close' instead.
+        self._h2_state.close_connection()
         self._state = HTTPConnectionState.CLOSED
         self._network_stream.close()