McCain, who had been a target of Trump's ire during his final year in the Senate, died Saturday at age 81.
Trump also said he has signed a proclamation to fly the U.S. flag at half-staff until McCain's final resting service, which will be held Sunday at the U.S. Naval Academy in Annapolis, Maryland.
The White House had garnered criticism for raising its flag Monday morning, even as other U.S. monuments and government sites kept their flags lowered — a long-standing symbol of national respect.
The White House once again lowered its flag on Monday afternoon, shortly before Trump ordered flags across the nation flown at half-staff "as a mark of respect for the memory and longstanding service" for McCain.