iCloud does not recognize Apple ID password

I changed my Apple ID password. I keep getting a pop-up that shows I need to sign-in to iCloud. iCloud does not recognize Apple password. A verification code is sent to my iPhone. I am not given a space to sign in and use the Apple password/verification code. So I bring up iCloud from System Preferences, and iCloud does not recognize the Apple password/verification code. My Apple ID password works for everything else i.e. AppStore, games, etc. How can this be fixed?