diff --git a/lib/vssh/libssh.c b/lib/vssh/libssh.c
index 5d5125b526..bde6355f73 100644
--- a/lib/vssh/libssh.c
+++ b/lib/vssh/libssh.c
@@ -921,7 +921,11 @@ static int myssh_in_AUTHLIST(struct Curl_easy *data,
           "keyboard-interactive, " : "",
           sshc->auth_methods & SSH_AUTH_METHOD_PASSWORD ?
           "password": "");
-  if(sshc->auth_methods & SSH_AUTH_METHOD_PUBLICKEY) {
+  /* For public key auth we need either the private key or
+     CURLSSH_AUTH_AGENT. */
+  if((sshc->auth_methods & SSH_AUTH_METHOD_PUBLICKEY) &&
+    (data->set.str[STRING_SSH_PRIVATE_KEY] ||
+     (data->set.ssh_auth_types & CURLSSH_AUTH_AGENT))) {
     myssh_to(data, sshc, SSH_AUTH_PKEY_INIT);
     infof(data, "Authentication using SSH public key file");
   }