Nor, he said, would the administration repay Iraqis who have worked and fought side by side with American troops by excluding them from the United States — as Mr. Trump initially did with an executive order shutting the door to citizens of seven mainly Muslim countries, including Iraq. That order has been stayed by the courts and is expected to be replaced soon.

“I have not seen the new executive order,” Mr. Mattis said on Sunday. “But right now, I’m assured that we will take steps to allow those who have fought alongside us to be allowed into the United States.”

As for Mr. Trump’s remarks during a visit to C.I.A. headquarters last month that the United States should have “kept” Iraq’s oil after the American-led invasion, and might still have a chance to do so, Mr. Mattis said that Americans were accustomed to paying for their fuel.

“We’re not in Iraq to seize anybody’s oil,” he told reporters in Abu Dhabi before departing for Baghdad.