Defense Secretary James Mattis is proving to be his own man.

On a trip to meet allies in Europe and the Middle East, the former Marine general again broke with his boss in public, telling Iraqi officials the U.S. military would not consider seizing the country’s oil, as President Trump has repeatedly suggested.

Mr. Mattis, who challenged Mr. Trump’s contention that the U.S. should resume torturing detainees in the war on terror in his first job interview in December, has broken with Mr. Trump several times on his current trip, denying the administration was in a war with the press, talking tough about Russia and its activities in Ukraine and now rejecting Mr. Trump’s idea of taking Middle East oil as a spoil of war.

“All of us here in this room, all of us in America, generally paid for our gas and oil all along, and I’m sure that we will continue to do so in the future,” Mr. Mattis said during a press conference in Abu Dhabi Sunday night.

“We’re not in Iraq to seize anybody’s oil,” he added.

Mr. Mattis followed up his Abu Dhabi stay with a surprise visit to Baghdad Monday, where Iraqi government troops, backed by U.S. forces, are preparing for an assault to drive Islamic State fighters from the western half of Mosul, the terror group’s last major urban stronghold in the country.

Iraqi President Haider al-Abadi announced the beginning of the western Mosul advance on Sunday. The assault to retake the western half of the city will be a much tougher slog than the four-month campaign to liberate eastern Mosul, experts say.

The estimated 2,000 to 2,500 fighters Islamic State has in western Mosul are backed by an elaborate defense system of tunnels, blast walls and entrenched fighting positions. Fighting in a dense urban environment, Iraqi army and paramilitary forces may be forced into a wrenching, block-by-block battle for the city.

Iraqi helicopters fired rockets at the village of Abu Saif early Monday, targeting a hill that overlooks the city’s airport, The Associated Press reported. By noon the forces entered the village and gained control over much of the strategic hill as fighting was still raging. Separately, militarized police in armored vehicles were moving toward the sprawling Ghazlani military base on the southwestern outskirts of the city.

Mr. Mattis, a highly decorated Marine who retired in 2013, has not been shy about pushing back against other elements of the Trump administration’s more controversial policy stances.

During his Senate confirmation hearing in January, Mr. Mattis said Russia was becoming an intractable problem for the U.S. and its allies, from its interference in the presidential election to overt efforts to “break” NATO.

Then-candidate Trump repeatedly stated his intent to forge closer political, economic and military ties with Russia. The White House has claimed publicly it has not ruled out military cooperation with Moscow in Syria to defeat Islamic State.

Mr. Mattis on Sunday even had kind words for the press, which Mr. Trump in a tweet over the weekend labeled the “enemy”: “The press, as far as I’m concerned, are a constituency that we deal with. I don’t have any issues with the press myself.”

Mr. Mattis traveled to Iraq as President Trump and his national security team are in the midst of a 30-day review ordered by the president to formulate a new strategy to defeat Islamic State in its Syrian and Iraqi strongholds. Mr. Mattis is expected to present the new plan to Mr. Trump in a week, and said his talks with Iraqi officials are part of that effort.

“We’re going to make certain that we’ve got good situational awareness of what we face as we work together and fight alongside each other,” Mr. Mattis told reporters traveling with him, according to the AP.

Mr. Trump has repeatedly vowed to eliminate the extremist group but has provided few details about how his approach might differ from that of the Obama administration, which had partnered with Syrian and Iraqi forces to drive Isalmic State out of several towns and cities.

• This article was based in part on wire service reports.

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