The U.S. State Department has ordered embassies to slow resettlement of refugees for the next few weeks and delay booking travel for refugees after March 3 as the numbers approach the annual cap of 50,000 set recently by President Donald Trump, according to American officials.

U.S. officials from embassies in the Middle East said they received a directive Tuesday from the State Department’s Population, Refugee and Migration bureau to delay booking travel to the U.S. for refugees awaiting final resettlement after March 3. The...