Secretary of Defense Jim Mattis visited Baghdad on Feb. 20. (Peter Stevenson/The Washington Post)

BAGHDAD — Defense Secretary Jim Mattis made his first trip to Iraq as Pentagon chief on Monday to determine what is needed to accelerate the campaign against the Islamic State, hours after rejecting a suggestion by President Trump that the United States might take Iraq’s oil.

“I think all of us here in this room — all of us in America — have generally paid for our gas and oil all along, and I am sure we will continue to do so in the future,” Mattis said during a meeting with reporters Sunday night. “We’re not in Iraq to seize anybody’s oil.”

Mattis’s rejection of the idea came after repeated claims by Trump that the United States should have taken Iraq’s oil during the Iraq War. Trump suggested last month that “maybe we’ll get another chance” to do so during a visit to the Central Intelligence Agency, generating new concerns about his position.

The defense secretary’s comments are one of several ways in which he has tried to sound a reassuring tone for allies since leaving Washington last week. In both Brussels and Munich, he promised audiences that the Trump administration will maintain its obligation to the North Atlantic Treaty Organization, which calls for all members to help if one is attacked, but warned that America might “moderate” its support in other ways to nations who do not meet defense spending guidelines set by NATO.

In Iraq, Mattis anticipates getting a better sense for the political situation, the enemy and the coalition’s Iraqi partners, he said. This visit comes with less than two weeks before Mattis, a retired Marine general and Iraq War veteran, is expected to deliver to the White House a set of recommendations that could include ordering more troops into Iraq or Syria or delegating more powers to battlefield commanders to streamline decision-making.

“We’re going to make sure we’re certain we’ve got good, shared situation awareness of what we face as we work together and fight alongside each other to destroy ISIS,” Mattis said.

One day before Mattis’s trip to Iraq, local forces there launched an offensive to take back the western side of Mosul, the country’s second-largest city. Militants seized it in June 2014 as they swept across the western and northern parts of the country and the Iraqi military crumbled. The government has since taken back several key cities, including Fallujah and Ramadi, and last month liberated the eastern half of Mosul.

Mattis said U.S. military advisers will have “the same role” that they did during the liberation of eastern Mosul on the western half of the city, an indication they will be near the front lines when Iraqi troops attack, but not directly involved in fighting unless something unexpected happens. Combat is expected to be fierce, with block-by-block engagements against fighters in thickly settled neighborhoods.

“The coalition forces are in support of this operation, and we will continue … with the accelerated effort to destroy ISIS,” Mattis said.

Mattis may also be asked by senior Iraqi officials to address the Trump administration’s plan to issue a new executive order that could restrict travel from some Middle Eastern and African countries. The first one, issued Jan. 27, caused a backlash as scores of people were detained at U.S. airports. It was suspended earlier this month in federal court, and a new “streamlined” version could be introduced within a week.

Mattis, who was surprised to find that the original version did not include any special considerations for Iraqi interpreters who served the U.S. military in combat, said Sunday that he has not seen a draft of Trump’s forthcoming executive order, but was given assurances that “we will take steps to allow those who have fought alongside us, for example,” to enter the country.

“They will have been vetted, obviously, by their performance on the battlefield as well as by the normal procedures, and I’m sure we’ll work through this quickly,” Mattis said.

The countries affected by the original ban were Iraq, Syria, Iran, Libya, Somalia, Sudan and Yemen.

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