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.