WASHINGTON — President Trump’s decision to impose his updated travel ban on Chad came over the objections of Pentagon and State Department officials, who argued that alienating the nation, one of America’s more reliable counterterrorism allies in Africa, risked harming long-term national security interests, administration officials said on Tuesday.

Mr. Trump accepted the recommendation of Elaine C. Duke, his acting secretary of Homeland Security, to include Chad in the travel ban after she wrote in a classified report that the country had done too little to crack down on Islamic extremists.

The president announced the travel restrictions after the White House’s Domestic Policy Council distributed Ms. Duke’s report to relevant agencies to seek input, according to officials at the State Department and the Pentagon. Officials at both departments were opposed to banning travelers from Chad, concerned about American interests, as were diplomats at the American embassy in the capital of N’Djamena, administration officials said.

But Stephen Miller, the president’s senior policy adviser, urged adoption of the entire list as recommended by Ms. Duke, officials said. They would not be named discussing internal deliberations.