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.
Trump and McCain had squabbled with each other as far back as July 2015, when then-candidate Trump mocked McCain's vaunted status as an American hero as being merely "because he was captured."
"I like people who weren't captured," Trump said, sparking a fierce backlash.
After McCain's death, politicians across the aisle released heartfelt statements of sympathy for McCain's family and gratitude for the late senator's service and character. But Trump's tweet only offered his sympathies for McCain's family.
Read Trump's full statement on McCain's passing below:
Despite our differences on policy and politics, I respect Senator John McCain's service to our country and, in his honor, have signed a proclamation to fly the flag of the United States at half-staff until the day of his interment.
I have asked Vice President Mike Pence to offer an address at the ceremony honoring Senator McCain at the United States Capitol this Friday.
At the request of the McCain family, I have also authorized military transportation of Senator McCain's remains from Arizona to Washington, D.C., military pallbearers and band support, and a horse and caisson transport during the service at the United States Naval Academy.
Finally, I have asked General John Kelly, Secretary James Mattis, and Ambassador John Bolton to represent my Administration at his services.