One of those options, which is said to be Mr. Trump’s choice, would keep a contingent of about 200 Special Operations forces at a few bases in eastern Syria, some near the Iraqi border, where they have been working alongside Syrian Kurdish partners.
Military officials also are expected to brief Mr. Trump this week on that plan and of the other counterterrorism options — including keeping some troops in Syria and using other commandos based in Iraq. Mr. Trump would need to approve any plan to leave forces in any part of Syria in addition to the about 150 in Al-Tanf, a small garrison in south-central Syria.
The commander of the so-called Syrian Democratic Forces, Mazlum Kobani, whose fighters switched sides to join Syrian government forces after Mr. Trump announced the American withdrawal, said on Saturday that despite the Turkish offensive, his troops had resumed counterterrorism operations near Deir al-Zour.
American officials widely interpreted the comments as a signal to Washington that the Syrian Kurds were still willing to fight in partnership with the United States against the Islamic State in eastern Syria, despite their abandonment in other parts of the country.
Some lawmakers suggested that it may be too late to contain the damage done to the counterterrorism mission and, more broadly, American credibility overseas. Representative Will Hurd, a Texas Republican on the House Intelligence Committee, described the cease-fire agreement announced on Thursday as “terms of surrender” to Turkey.
Also appearing on “Face the Nation,” Mr. Hurd, a former C.I.A. officer, referred to Turkey, a NATO ally, as part of a group of American “enemies” and “adversaries” who will benefit from the cease-fire agreement.
“Our enemies and our adversaries like Iran, Russia, Turkey, they’re playing chess,” he said. “Unfortunately, this administration is playing checkers.”