“The last 24 hours are a grim reminder of why we should not underestimate ISIS and how badly the pesh merga need more ground support in addition to continued air support,” said Masrour Barzani, the chairman of the Kurdish region’s security council.

After his meeting with Massoud Barzani, the president of the Kurdish autonomous region, Mr. Carter signaled that the Obama administration would accelerate some arms deliveries to the Kurds, though that falls short of what Kurdish officials would like.

The United States had promised to provide the weapons and equipment for two new combat brigades if the Kurds followed through with plans to establish units that would integrate fighters from the Kurds’ two main political parties: the Kurdistan Democratic Party and the Patriotic Union of Kurdistan.

But the Kurds have contended that forming the new brigades would be costly and time-consuming. So Mr. Carter said the Obama administration now planned to move ahead anyway with the delivery of the equipment, which is stored in Kuwait. The expectation, Mr. Carter made clear, is that the equipment will be used by the Kurds for the “encirclement of Mosul” after Iraqi forces retake Ramadi from the Islamic State.

During his visit here, Mr. Carter also met with several Special Forces commandos who were among the 50 who recently traveled to northern Syria to work with Syrian fighters and Kurdish forces there. A senior Defense Department official, who asked not to be identified in order to discuss a closed-door meeting, said that Mr. Carter was encouraged by their assessment of the effort to build a Syrian Arab force that could put pressure on Raqqa, the de facto capital of the Islamic State’s territory.

The landscape in northern Iraq is a complicated one. One coalition official, who spoke on the condition of anonymity to discuss intelligence reports, said that in recent weeks Turkey had sent about 1,000 troops, and a small number of tanks, to reinforce about 200 Turkish soldiers who have been involved in training local fighters.

The presence of the Turkish forces has been a major source of friction between Iraq and Turkey, and they were caught up in the recent fighting.