WASHINGTON—President Trump is re-evaluating a rapid pullout of U.S. troops from Syria but remains committed to pursuing the withdrawal he announced earlier this month, Sen. Lindsey Graham said Sunday after a White House meeting.

“I think we’re slowing things down in a smart way,” Mr. Graham (R., S.C.) said. “But the goal has always been the same: To be able to leave Syria, to make sure ISIS never comes back, our partners are taken care of and Iran’s contained.”

The...