Apple wants me to verify my account but I don't want to enter card details!

BEWARE This might be a phishing or scam attempt to get your information. You should not click on links in the text. Is that how you got to the verification page?

Don't "verify" yourself on that page. Apple does not suspend your account just because they can't "verify" you. You can check this by going to id.apple.com and logging in your account - can you log in? Then nothing has been suspended. You can try downloading a free app from the App store as well - you should be able to buy/download no problem. IF you get a message that says you can't download or buy because of whatever issue, then you can call Apple Support and they can unlock your account over the phone, assuming there is not some overdue balance that needs to be paid.

They will, however, disable your account for instances where you have put your password in wrong too many times. The only way to get by an account "disabled for security reasons" is to change the password.

TL;DR don't put your CC information into this site. It's phishing.

I agree with javaliga, this could be a phishing scam. I would try logging out of the iTunes store, doing a forced restart, and logging back in. That would be the safe way to do it. I would delete the text.

Sign out of the iTunes Store (in Settings).

Forced restart. Hold down the Home and Wake/Sleep buttons at the same time for about 15-20 seconds until the Apple logo appears.

Then sign back into the iTunes Store.

If you did get to a "verification page" by clicking on a link AND entered your Apple ID & password info (even though you did not enter any credit card info), I suggest you change your Apple ID password IMMEDIATELY:

Change your Apple ID password - Apple Support

Apple does not send SMS messages for account issues.

This IS a scam and IS getting reported in the press worldwide