But the fact that General Mladic was finally brought to justice, nearly a quarter century after the crimes he committed in the former Yugoslavia, attests to the hurdles that stand in the way of a full moral reckoning with episodes of genocide and mass atrocities.

The Trump administration has more immediate goals in mind in calling the Rohingya crackdown “ethnic cleansing.” Mr. Tillerson said the United States wanted Myanmar’s government to put in place conditions that would allow refugees to return from Bangladesh to Rakhine State.

Since late August, more than 620,000 Rohingya have fled Myanmar, which is majority Buddhist, for Bangladesh. Only about one-third of the Rohingya who lived in Myanmar now remain in the country. A recent report by Human Rights Watch said there was also evidence of widespread rape of Rohingya women and girls by uniformed members of the military.

Human rights advocates said the administration’s use of the label “ethnic cleansing” would add to an international pressure campaign against Myanmar that they hope will come to include a global arms embargo and a suspension of military-to-military relations.

Legislation in Congress would require the United States to cut off all ties to the military. Lawmakers praised Mr. Tillerson’s statement, though some labeled it overdue.

“We cannot let another massacre occur as the world stands by and watches,” said Senator John McCain, the Arizona Republican who is chairman of the Armed Services Committee. “The United States has a moral obligation to do all it can to prevent mass atrocities and make clear to those responsible for ethnic cleansing in Burma — and those who look to do the same elsewhere — that their actions will not be tolerated.”

Mr. Tillerson’s announcement was also welcomed at the United Nations, where senior officials began describing the anti-Rohingya atrocities as ethnic cleansing more than two months ago.