Apple ID verification failed

Under the settings option on the phone, the message shows "Update Apple ID Settings". When I update, the screen shows my apple ID and asks for the password. After giving the correct password, the message displayed is "Verification Failed, An unknown error occurred". I am giving the valid password because I could successfully log in using the same apple ID and password to my iCloud account and https://appleid.apple.com website.

How to overcome the error message?