BAGHDAD - The US military is not in Iraq "to seize anybody's oil," Defense Secretary Jim Mattis said, distancing himself from remarks by President Donald Trump at the start of a visit to Iraq on Monday.Mattis, on his first trip to Iraq as Pentagon chief, is hoping to assess the war effort as US-backed Iraqi forces launch a new push to evict Islamic State militants from their remaining stronghold in the city of Mosul.But he is likely to face questions about Trump's remarks and actions, including a temporary ban on travel to the United States and for saying America should have seized Iraq's oil after toppling Saddam Hussein in 2003.Trump told CIA staff in January: "We should have kept the oil. But okay. Maybe you'll have another chance."Mattis, however, flatly ruled out any such intent. "We're not in Iraq to seize anybody's oil," he told reporters traveling with him.His remarks are the latest example of his policy differences with Trump. Trump has acknowledged that Mattis did not agree with him about the usefulness of torture as an interrogation tactic but, in a sign of Mattis' influence, said he would defer the matter to his defense secretary.Mattis has also been more critical than Trump of Russian President Vladimir Putin, and distanced himself from Trump's labeling of the media as "the enemy of the American people," saying he had no problems with the press.A retired Marine general who led American troops in Iraq, Mattis has also sought an exemption from Trump's travel ban for Iraqis who served with US troops, including translators.He said he had not seen a new executive order which the administration is considering. "But I right now am assured that we will take steps to allow those who have fought alongside us, for example, to be allowed into the United States," Mattis said.MOSUL CAMPAIGNMattis is finalizing plans at Trump's request to accelerate the defeat of Islamic State and is expected to meet senior US and Iraqi officials in Iraq.His visit comes a day after Iraqi Prime Minister Haider al-Abadi announced the start of the ground offensive on western Mosul, where Islamic State militants are essentially under siege along with an estimated 650,000 civilians.The insurgents were forced out of the east of the city last month after 100 days of fighting.The US commander in Iraq, Army Lieutenant General Stephen Townsend, has said he believes US-backed forces will recapture both of Islamic State's major strongholds - Mosul and the city of Raqqa in Syria - within the next six months.The defense secretary's strategy review could lead to additional deployment of US forces, beyond the less than 6,000 American troops deployed to both Iraq and Syria today. Experts say the Pentagon may also look at increasing the number of attack helicopters and air strikes and bringing in more artillery, as well as granting greater authority to battlefield commanders fighting Islamic State.The future for US forces in Iraq, and for Iraq's fragmented society, is unclear once the hardline Sunni group has been expelled from Mosul.Mattis told the Senate last month that the top US goal in Iraq should be "to ensure that it does not become a rump state of the regime in Tehran," which has close ties with the Shi'ite political elite ruling Iraq.A power struggle appears to be taking root between Iraq's Shi'ite leaders. Influential cleric Moqtada al-Sadr, who is openly hostile to Washington's policies in the Middle East, has begun mobilizing supporters ahead of parliamentary and provincial elections.Sadr on Monday said the government should demand the withdrawal of US and allied forces after the battle of Mosul."The Iraqi government has to demand that all occupying and so-called friendly forces leave Iraq in order to preserve the prestige and the sovereignty of the state," he said.Sadr's main rival is former prime minister Nuri al-Maliki, a pro-Iranian politician re-emerging as a possible kingmaker or even for a return to the premiership itself.