Help with "Your config.php file does not appear to have the proper file permissions"

I set permissions via SFTP to 666 on config.php and database.php but am getting this in the installation wizard:

Your config.php file does not appear to have the proper file permissions. Please set the file permissions to 666 (or the equivalent write permissions for your server) on the following file: expressionengine/config/config.php

Running ls -l on the command line I can see the permissions are assigned to me as a user. Could the problem be that the permissions need to be set in a different way for the server to access the files? Or something else?