diff --git a/flask_oauthlib/client.py b/flask_oauthlib/client.py
index e40042a2..50a1b931 100644
--- a/flask_oauthlib/client.py
+++ b/flask_oauthlib/client.py
@@ -231,11 +231,6 @@ def __init__(
         self.oauth = oauth
         self.name = name
 
-        if (not consumer_key or not consumer_secret) and not app_key:
-            raise TypeError(
-                'OAuthRemoteApp requires consumer key and secret'
-            )
-
         self._base_url = base_url
         self._request_token_url = request_token_url
         self._access_token_url = access_token_url
@@ -251,6 +246,26 @@ def __init__(
         self.app_key = app_key
         self.encoding = encoding
 
+        # Check for required authentication information.
+        # Skip this check if app_key is specified, since the information is
+        # specified in the Flask config, instead.
+        if not app_key:
+            req_params = self.request_token_params or {}
+            if req_params.get("signature_method") == oauthlib.oauth1.SIGNATURE_RSA:
+                # check for consumer_key and rsa_key
+                rsa_key = req_params.get("rsa_key")
+                if not consumer_key or not rsa_key:
+                    raise TypeError(
+                        "OAuthRemoteApp with RSA authentication requires "
+                        "consumer key and rsa key"
+                    )
+            else:
+                # check for consumer_key and consumer_secret
+                if not consumer_key or not consumer_secret:
+                    raise TypeError(
+                        "OAuthRemoteApp requires consumer key and secret"
+                    )
+
     @cached_property
     def base_url(self):
         return self._get_property('base_url')
@@ -321,7 +336,8 @@ def make_client(self, token=None):
                 params["resource_owner_secret"] = token[1]
 
             client = oauthlib.oauth1.Client(
-                self.consumer_key, self.consumer_secret,
+                client_key=self.consumer_key,
+                client_secret=self.consumer_secret,
                 **params
             )