President Trump has given no indication that he has made a decision about how to proceed, as diplomatic talks continue.
President Trump threatened to strike Iran, but the military has needed time to build up its forces in the region.
The moves appear to highlight lingering doubts in Washington about the new Syrian government’s ability to ensure security.
The military base at Al-Tanf had hosted U.S. troops fighting against the Islamic State since 2016. Some of the troops are expected to be repositioned at a Jordanian military base across the border.
A U.S. fighter jet shot down the Iranian drone after it “unnecessarily maneuvered” toward the Abraham Lincoln aircraft carrier.
There is little sign that Iran has made significant progress in reconstituting its nuclear program, leaving questions about the timing and motive behind potential plans for further attacks.
Protests that erupted late last year shook elements of the Iranian government, according to the reports.
President Trump said the United States was “watching Iran” and sending a naval force there, despite also saying that his threats had halted executions.
The U.S. military said it had transferred 150 Islamic State detainees from northeastern Syria to Iraq and could eventually move as many as 7,000, as the Syrian government assumes control of the region from Kurdish-led forces.
Prime Minister Benjamin Netanyahu of Israel asked the president to postpone any planned attack. Israeli and Arab officials fear Iran could retaliate by striking their countries.