HONG KONG—The U.S.'s crackdown on global tax evaders is prompting some Americans in Asia to rethink their citizenship, attorneys there say, in part amid an increasing burden of paperwork required by U.S. tax law.

"When I became an immigration lawyer 30 years ago, people really were excited about going to America. Now, more than half of my clients are people thinking of other alternatives rather than people seeking to immigrate to America," said Eugene Chow, the principal of Chow King & Associates in Hong Kong. "My mentor, who is in his early 80s, said to me, 'You became an immigration lawyer to fulfill the American dream, and now you are helping people leave.' "

While the numbers of those renouncing their U.S. citizenship are small—more than 1,000 people in the second quarter of 2013, out of more than six million Americans estimated to be living abroad—the numbers have climbed this year, according to recently released figures.

The main trigger for cutting ties with U.S., several lawyers say, is the Foreign Account Tax Compliance Act, or Fatca, which requires foreign institutions to disclose the overseas assets of U.S. green-card holders and citizens to the U.S. government. The main objective of Fatca is to identify people who may be evading taxes through offshore investment vehicles.

A growing number of wealthy Americans in Asia—and others with green cards—are exploring whether to renounce their U.S. citizenship or give up their green cards to avoid onerous tax obligations.