The acting United States defense secretary, Patrick M. Shanahan, arrived in Baghdad early Tuesday for an unannounced visit with Iraqi leaders to discuss the American troop presence in the country and the fight against the remains of the Islamic State.
Mr. Shanahan’s trip coincides with plans for an American troop withdrawal from Syria and questions about whether some of those troops could instead be based in Iraq, which would be used as a base for operations in Syria.
His quest was complicated — or, perhaps, made necessary — by an interview President Trump gave this month suggesting American troops could be sent to Iraq to keep an eye on neighboring Iran, a fellow Shiite state.
Since then, Iraqi politicians, many sympathetic to the Iranians, have been up in arms, saying that a foreign government has no right to use Iraqi territory to attack a neighboring state.
The Pentagon, in a statement that seemed aimed at calming the concerns over Mr. Trump’s comments on Iran, said that Mr. Shanahan and the Iraqi prime minister, Adel Abdul Mehdi, had reaffirmed “the growing bilateral security relationship” between their countries and noted that the “partnership is based on defeating ISIS.”
There are still around 2,000 American troops in Syria, many of them special operations forces fighting Islamic State militants alongside Syrian Kurdish soldiers. They have drastically cut into the Islamic State’s territory, save one or two pockets of militants in the far east of Syria. But Mr. Trump has ordered the troops to leave the fighting to other players, including the Syrian Army, the Russians who are fighting with them, and the Turks.
Military leaders have resisted the order, both because they say that the Islamic State still poses a threat and that a retreat now would mean abandoning the Syrian Kurds, whom the Americans have in many cases armed, trained and fought alongside.
Turkey regards the Syrian Kurds, the Syrian Democratic Forces, as the military arm of the P.K.K., an outlawed Kurdish terrorist group, in Ankara’s eyes. The Turks have made little effort to conceal their intent to drive them far from the Turkish border, and possibly out of Syria entirely.
As he left Washington, Mr. Shanahan did not say whether he would ask Iraq to host some of the special operations troops now fighting in Syria. However, there has been discussion about that possibility in military circles both in Baghdad and Washington. From there, theoretically, they could help finish off the Islamic State and give support to the Syrian Kurdish troops.
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There are currently about 5,200 American troops in Iraq, engaged primarily in training the Iraqi military and sometimes helping Iraqi troops by providing reconnaissance and air support in their fight against Islamic State fighters in Iraq. Although there has been a drastic drop in the number of Islamic State attacks in Iraq, there are still at least one or two every day.
Among several competing ideas for the United States forces coming to Iraq from Syria, commanders seem to favor leaving several hundred special operations forces near the Syrian border so they can have easy access to Syria.
But things were complicated by Mr. Trump’s statement that he wanted to keep American forces in Iraq to keep an eye on Iran.
In response to the president’s remarks, Iraqi politicians accelerated discussions of a law that would strictly limit the number of American troops allowed, their activities and the duration of their stay.
The antagonism is hardly surprising, as Iran has been actively lobbying in Iraq and reaching out to both Shiite and Sunni Muslims on a variety of issues. The Iranians are eager to avoid any increase in the United States troop presence in Iraq or having more American troops posted near its border. Currently, only a few small contingents of Americans are active in eastern Iraq, where they are helping the Iraqi Army fight pockets of Islamic State resistance.
Until Mr. Trump visited Al Asad Air Base in December, highlighting the American presence in the country, the American military had kept a low profile, working closely with the Iraqi Army against the Islamic State. However, Mr. Trump’s visit, which did not include a meeting with Iraqi political figures, although he spoke to the prime minister by telephone, angered Iraqis who saw his attitude as presumptuous.