diff --git a/src/mcp/server/__init__.py b/src/mcp/server/__init__.py
index ae78f367c..de155ac81 100644
--- a/src/mcp/server/__init__.py
+++ b/src/mcp/server/__init__.py
@@ -12,6 +12,7 @@
 from mcp.server.session import ServerSession
 from mcp.server.stdio import stdio_server as stdio_server
 from mcp.shared.context import RequestContext
+from mcp.shared.exceptions import McpError
 from mcp.shared.session import RequestResponder
 
 logger = logging.getLogger(__name__)
@@ -331,8 +332,8 @@ async def run(
         read_stream: MemoryObjectReceiveStream[types.JSONRPCMessage | Exception],
         write_stream: MemoryObjectSendStream[types.JSONRPCMessage],
         initialization_options: InitializationOptions,
-        # When True, exceptions are returned as messages to the client.
-        # When False, exceptions are raised, which will cause the server to shut down
+        # When False, exceptions are returned as messages to the client.
+        # When True, exceptions are raised, which will cause the server to shut down
         # but also make tracing exceptions much easier during testing and when using
         # in-process servers.
         raise_exceptions: bool = False,
@@ -367,6 +368,8 @@ async def run(
                                         )
                                     )
                                     response = await handler(req)
+                                except McpError as err:
+                                    response = err.error
                                 except Exception as err:
                                     if raise_exceptions:
                                         raise err