Senator Lindsey Graham of South Carolina, a vocal Republican critic of President Trump’s plan for a 30-day troop withdrawal of American troops from Syria, suggested on Sunday that the pullout had been slowed and that he felt “a lot better” about it after a lunch with the president.

“I think we’re in a pause situation where we are re-evaluating what’s the best way to achieve the president’s objective of having people pay more and do more,” Mr. Graham said.

He did not elaborate on what that meant. But he may have been referring to assurances that Mr. Trump is said to have given some military officials that they can have more time than 30 days to ensure a proper drawdown of troops.

Mr. Trump’s surprise announcement on Twitter this month that he planned to withdraw the 2,000 American troops in Syria over the advice of military officials drew strong objections from many of his usual allies, like Mr. Graham, and helped prompt Defense Secretary Jim Mattis to resign.