“That is something we have got to figure out,” he added.

With an increase in reports of civilian casualties from the American bombing of Islamic State targets in Iraq and Syria, some human rights groups have questioned whether the rules of engagement have been loosened since President Trump took office.

Pentagon officials said this week that the rules had not changed. But General Townsend said on Tuesday that he had won approval for “minor adjustments” to rules for the use of combat power, although he insisted they were not a factor in the Mosul attack.

General Townsend acknowledged, however, that steps had been taken to speed up the process of providing air power to support Iraqi troops and their American Special Operations advisers at the leading edge of the offensive to recapture Mosul from the Islamic State. The goal, he said, was to “decentralize” decision-making.

General Townsend did not describe the changes in detail, but he cast them as a return to the military’s standard offensive doctrine, in contrast to the “very centralized” approach he said was initially put in place after President Barack Obama sent American forces back to Iraq to combat the Islamic State, also known as ISIS or ISIL.

Maj. Gen. Maan al-Saadi, an Iraqi special forces commander, has said that his men called in a coalition airstrike to take out snipers on the roofs of three houses in a Mosul neighborhood called Mosul Jidideh. The Iraqi forces, General Saadi said, were unaware that at least some of the houses were filled with civilians.