Two weeks ago, the American military finally acknowledged what nongovernmental monitoring groups had claimed for months: The United States-led coalition fighting the Islamic State since August 2014 has been killing Iraqi and Syrian civilians at astounding rates in the four months since President Trump assumed office. The result has been a “staggering loss of civilian life,” as the head of the United Nations’ independent Commission of Inquiry into the Syrian civil war said last week.

“At least 484 civilians have been unintentionally killed by coalition strikes,” the United States Central Command, or Centcom, the military command responsible for the Middle East, said in a June 2 statement. Four months earlier, Centcom had said at least 199 civilians had been killed up to that point in the bombing campaign. Estimates by independent monitors are much higher. Airwars, a watchdog group, says coalition airstrikes have killed nearly 4,000 civilians.

The civilian death toll has risen mainly because the battle has moved deeper into major cities. But even as the civilian death toll ticks upward, the American military has relaxed oversight, investigation and accountability on civilian casualties. Finding out the reasons for these tragic mistakes, seeing what can be learned from them and enforcing the American military’s own standards could save thousands of lives.

Mr. Trump has given the military “total authorization” to decide how, and how much, force will be used, authority that was more closely held by the Obama White House. But Secretary of Defense James Mattis insisted on May 28 that the rules of engagement have not changed. “There is no relaxation of our intention to protect the innocent,” he said.