BAGHDAD — The American-led military coalition in Iraq said Friday that it was investigating reports that scores of civilians — perhaps as many as 200, residents said — had been killed in recent American airstrikes in Mosul, the northern Iraqi city at the center of an offensive to drive out the Islamic State.

If confirmed, the series of airstrikes would rank among the highest civilian death tolls in an American air mission since the United States went to war in Iraq in 2003. And the reports of civilian deaths in Mosul came immediately after two recent incidents in Syria, where the coalition is also battling the Islamic State from the air, in which activists and local residents said dozens of civilians had been killed.

Taken together, the surge of reported civilian deaths raised questions about whether once-strict rules of engagement meant to minimize civilian casualties were being relaxed under the Trump administration, which has vowed to fight the Islamic State more aggressively.

American military officials insisted on Friday that the rules of engagement had not changed. They acknowledged, however, that American airstrikes in Syria and Iraq had been heavier in an effort to press the Islamic State on multiple fronts.