diff --git a/fastapi/dependencies/utils.py b/fastapi/dependencies/utils.py
index d35aa1b36..1644c59e0 100644
--- a/fastapi/dependencies/utils.py
+++ b/fastapi/dependencies/utils.py
@@ -757,5 +757,6 @@ def get_body_field(*, dependant: Dependant, name: str) -> Optional[ModelField]:
     return final_field
 
 
-def get_path_hash_val(path: str, methods: Optional[Set[str]]) -> str:
+def get_path_hash_val(path: str, methods: Optional[Set[str]] = None) -> str:
+    methods = methods or {"GET"}
     return f"path:{path};methods:{methods}"
diff --git a/fastapi/routing.py b/fastapi/routing.py
index a923cd29f..58ee9adb5 100644
--- a/fastapi/routing.py
+++ b/fastapi/routing.py
@@ -677,6 +677,10 @@ class APIRouter(routing.Router):
             name=name,
             dependency_overrides_provider=self.dependency_overrides_provider,
         )
+        hash_val = get_path_hash_val(route.path)
+        if hash_val in self.added_routes:
+            raise RouteAlreadyExistsError(route.name)
+        self.added_routes.add(hash_val)
         self.routes.append(route)
 
     def websocket(
@@ -781,7 +785,7 @@ class APIRouter(routing.Router):
                 )
             elif isinstance(route, routing.Route):
                 methods = list(route.methods or [])
-                hash_val = get_path_hash_val(route.path, route.methods)
+                hash_val = get_path_hash_val(prefix + route.path, route.methods)
                 if hash_val in self.added_routes:
                     raise RouteAlreadyExistsError(route.name)
                 self.added_routes.add(hash_val)