When it asked for your password did you type it in? You can also try signing out of iCloud on the phone and then signing back in again.
My husband got the same message on both his phone and his Mac, and once I typed in the password, they went away. On the phone, I typed it in incorrectly the first time (easy to do with a miniature keyboard), but the second time I typed it in and verified each letter and character as I typed it, and it signed it on with no issues (that's how I know I mis-typed something the first time).
Again, if you sign out of iCloud and back in, it should resolve the issue.
Cheers,
GB