WASHINGTON — President Trump has yet to follow through on a threat to cut off hundreds of millions of dollars in annual aid to three Central American nations from which migrants and refugees are moving toward the United States border, according to the head of the main American foreign aid agency.

“I’m not aware of firm decisions being made,” Mark Green, the administrator of the United States Agency for International Development, said Friday during a wide-ranging interview at his office a few blocks southeast of the White House. “I know it’s under review.”

The lack of action calls into question whether Mr. Trump actually intends to punish the three countries, Guatemala, Honduras and El Salvador, for failing to stop the migrants, or whether his remarks are just political grandstanding. With Republican control of the House in peril in the midterm elections on Tuesday, the president has escalated his anti-immigrant messaging to appeal to voters.

The aid agency, known as U.S.A.I.D., has supplied data to White House officials that lay out programs and amounts of aid given to those three countries, as is typical.