“This is not about Syria and Iraq,” General Dunford said at the Brookings Institution in Washington. The Islamic State, he noted, at one point numbered 45,000 foreign fighters from more than 100 countries. “Our plan, to be successful, needs to, No. 1, cut the connective tissue between regional groups that now form a transregional threat.”

Mr. Mattis will probably present Mr. Trump a range of options that include loosening some battlefield restrictions and allowing American troops to get closer to the fight. He may also recommend putting a limited number of additional troops on the ground in Syria.

But Pentagon officials said there was little appetite in the Defense Department for a full-fledged American military mission in Syria that would include thousands of additional combat troops. Any such move could leave the United States responsible for picking up the pieces after a defeat of the Islamic State.

General Dunford said the Pentagon’s goal was to outline the options for dealing with the Islamic State while at the same time making clear “the risks associated with each one.”