“As Mosul falls, everyone [in ISIS] will move out,” argues a senior Trump administration official. “ISIS will fall back into different areas. You could get suicide attacks again in Ramadi,” an Iraqi city that was liberated 14 months ago.

But many experts outside the administration see many holes in Trump’s counterterrorism approach and worry that it could backfire. His rhetoric about “Islamic terrorism” has turned up the ideological heat, but it has frightened some potential Muslim allies at home and abroad. Trump has denounced the Obama administration’s allegedly weak strategy — which, however cautious, was slowly throttling ISIS — without having a clear alternative.

The travel ban has offended the Iraqi government, for example, even as its elite forces bravely captured eastern Mosul. The casualty rate among the Iraqi Counterterrorism Service, which has done most of the heavy fighting, is about 30 percent, according to a high-level intelligence official. Because that unit must rebuild its strength, victory in Mosul is at least six months away.