A burned Rohingya village in Burma. (Soe Zeya Tun/Reuters)

HAVING ENGINEERED a horrific campaign of ethnic cleansing against the Muslim Rohingya minority, the Burmese military has turned its attention to another persecuted group. An offensive against the mostly Christian Kachin people near Burma’s northern border is underway, backed by aircraft and artillery. As the Wall Street Journal reported, the attack is employing some of the same military units that earlier burned villages and committed mass killings and rapes in Rakhine state, driving 680,000 Rohingya across the border to Bangladesh. The State Department’s ambassador on religious freedom this week said there had been a doubling down on the persecution of Burma’s non-Buddhist citizens. “The situation,” Sam Brownback said, “is dire.”

The Tatmadaw, as the military is known, feels free to pursue this genocidal policy because it has suffered virtually no consequences for what human rights groups and senior U.N. officials describe as blatant crimes against humanity. The State Department labeled the campaign against the Rohingya “ethnic cleansing,” but the Trump administration has so far imposed sanctions on just one general; we’re told that 10 others have been identified by State, but there has been no follow-through. China has blocked action by the U.N. Security Council . If President Trump is aware of the crisis, he hasn’t shown it.

The relative good news is that there has been a concerted and bipartisan movement in Congress to demand accountability from the Burmese military. Last week the House passed, in a lopsided 382-to-30 vote, legislation to require the administration to compile a list of Burmese officials involved in the ethnic cleansing and impose sanctions on them. The Senate Foreign Relations Committee approved a similar bill in February. A Senate floor vote on either measure would almost certainly result in another big margin in favor.

The measure is nevertheless in danger of stalling. The Senate Armed Services Committee has not attached the Burma sanctions to the annual defense authorization act, as happened last week in the House. Meanwhile, the stand-alone legislation, sponsored by Sens. John McCain (R-Ariz.) and Benjamin L. Cardin (D-Md.), has been held up by Majority Leader Mitch McConnell (R-Ky.). Mr. Cardin is expected to offer a floor amendment to the defense bill, but that could be blocked by a single senator.

Mr. McConnell, a longtime champion of Burma’s Nobel Prize-winning civilian leader, Aung San Suu Kyi, is said to be wary of measures that might weaken her elected government. But, as has become increasingly clear over the past 10 months, when it comes to the assault on the Rohingya, Aung San Suu Kyi is part of the problem. She has failed to condemn the ethnic cleansing, and occasionally even defended it.

Other senators have expressed concern that sanctions on the generals will only harm their relations with the United States without changing behavior. But it was U.S. sanctions that induced the Tatmadaw to allow a limited democratic opening in 2015; and the new measures, which could be waived by the White House, would not harm the economy or general population.

Calculations about what Burma’s generals might do or not do in response to sanctions are ultimately beside the point. Grave crimes have been carried out against defenseless civilians. If there is no serious response, the atrocities will be repeated — and not only in Burma.