The European principalities of Andorra and Liechtenstein pledged to relax their bank-secrecy laws, yielding to international pressure on tax havens to stop shielding the holdings of the rich.

The moves raise the stakes for big tax-haven centers such as Switzerland to take similar steps before the coming meeting of the Group of 20 developed and emerging nations in London. Offshore tax evasion is expected to be a topic at the April 2 summit.

The...