BAGHDAD — Defense Secretary James Mattis arrived in Baghdad on Monday, promising that, despite what President Trump said last month, the administration would not try to seize Iraq’s oil.

He also said the administration would not bar US border entry to Iraqis who have worked and fought side by side with American troops.

Trump has signed 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,’’ 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 Trump’s remarks during a visit to CIA 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, 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.

That Mattis would even have to make such comments would have been unthinkable under previous administrations.

But many once-unthinkable things have become par for the course under Trump, and his emissaries abroad are spending much of their time trying to reassure American allies.

Mattis was the first senior official in the Trump administration to visit Iraq.

In Brussels last week, Mattis assured NATO members that, contrary to what his boss had said, the United States still valued the trans-Atlantic alliance. In Munich, he had the same message for skittish European diplomats assembled for a major annual conference on security.

Nowhere have Trump’s policy pronouncements landed harder, though, than in Iraq, where about 5,000 American troops are assisting Iraqi forces in the fight against the Islamic State.

A former Iraqi ambassador to Washington, Lukman Faily, said last month that Iraqis were unsettled by Trump’s moves, including the travel ban, and wondered whether the United States even wanted a long-term relationship with Iraq.

While in Baghdad, Mattis plans to hold talks with Iraqi officials as well as American military commanders.

“I need to get current on the situation’’ in Iraq, he said. “And the only way you can do this is talking to the people on the ground.’’ He added that American-backed coalition forces fighting the Islamic State would “continue with the accelerated effort to destroy’’ the Islamic State.