AMMAN, Jordan — President Trump, who has been accused by lawmakers of dragging his feet on Afghanistan, has settled on a new strategy to carry on the nearly 16-year-old conflict there, administration officials said Sunday. The move, following a detailed review, is likely to open the door to the deployment of several thousand troops.

“The president has made a decision,” Defense Secretary Jim Mattis told reporters on an overnight flight that arrived in Amman, Jordan, on Sunday. “I am very comfortable that the strategic process was sufficiently rigorous.”

Mr. Mattis declined to say what steps the president had ordered, including on troop levels, saying that the president wanted to outline the new approach himself.

The defense secretary received the authority in June to send as many as 3,900 troops to Afghanistan so that the United States military could expand its efforts to advise Afghan forces and support them with American artillery and airpower. But Mr. Mattis has refrained from building up the American force there until the Trump administration agreed on a broader strategy.