Update on this matter - I was able to book US domestic flight with UA online on TK.

Here is the situation - you need to enter your card in your profile and save it. Once saved, take a careful look at the card in the payment methods and make sure that it correctly displays the issuing bank,

In my case it is Chase United Explorer and I see card as 'Card Type CHASE BANK USA. NATIONAL ASSOC' in the profile.

If your card is displayed as 'unknown' most likely the transaction won't go thru.