It was unclear how the local government would enforce the rule, and the announcement could be as much about playing to the country’s Buddhist majority as about actual policy. It was also unclear what effect the new limits would have; there have already been restrictions on Rohingyas marrying, which analysts said were meant to decrease the birthrate.

A spokesman for Rakhine State, Win Myaing, said the new program was meant to stem rapid population growth in the Muslim community, which a government-appointed commission identified as one of the causes of the sectarian violence.

Although Muslims are the majority in the two townships in which the new policy applies, they account for only about 4 percent of Myanmar’s roughly 60 million people. The measure was enacted a week ago, after the commission recommended family planning programs to stem population growth among Muslims, Mr. Win Myaing said. “Overpopulation is one of the causes of tension,” he said.

The policy will not apply yet to other parts of Rakhine State, which have smaller Muslim populations. The central government has not made any statement about the two-child policy, which was introduced at a local level. Calls seeking comment on Saturday from two government spokesmen were not immediately returned, but an official with Rakhine State, Myo Than, said all local policies require “consent from the central government.”

A new wave of sectarian violence in Myanmar first flared nearly a year ago in Rakhine State between the region’s Rakhine Buddhists and Muslim Rohingya. Mobs of Buddhists armed with machetes razed thousands of Muslim homes, leaving hundreds of people dead and forcing 125,000 to flee, mostly Muslims.