The 81-year-old McCain, a former prisoner of war in Vietnam who was the Republican nominee for president in 2008, passed away on Saturday at his home in Arizona after a battle with brain cancer.
Mr. McCain, who served as a senator from Arizona for more than 30 years, clashed repeatedly with Mr. Trump even though they were both Republicans, and the president initially paid scant tribute to the senator after his death.
He had previously refused to sign the proclamation which would order the American flag to remain at half-mast until the funeral.
"Finally, I have asked General John Kelly, Secretary James Mattis, and Ambassador John Bolton to represent my Administration at his services".
McCain's body will lie in state in the Capitol Rotunda in Washington before a procession passing by the Vietnam Veterans Memorial.
The service at the National Cathedral in Washington will feature eulogies by former Presidents Barack Obama and George W. Bush. The White House had lowered its flag to half-staff on Sunday, but shortly after midnight, it was back at full staff, in a clear break with precedent - which dictates that it be lowered until burial - and the US flag code.
"The president will not be, as far as we know, attending the funeral".
First Lady Melania Trump thanked the late Senator John McCain for his service.
"Like most people, I have regrets". It was McCain who stopped Trump's repeal of Obamacare and Trump referred to the veteran as "not a war hero".
"If the president put out a flowery statement about John McCain's life, the media would criticize it and say it's not consistent with the other things he's said in the past, and it would become a story about the president", Short said during an appearance on CNN.
President Donald Trump issued a statement on August 27, about the passing of Sen.
The U.S. Department of Homeland Security had issued a government-wide notification after McCain's death to lower flags at U.S. facilities but rescinded it on Monday, leaving the decision to staff at individual sites, according to an official.
"Do not despair of our present difficulties, but believe always in the promise and greatness of America, because nothing is inevitable here", McCain went on to write. Trump's proclamation came just hours after the White House flag had been returned to full-staff, drawing complaints from right and left.
"It is atrocious", Mr Mark Corallo, a former spokesman for Mr Trump's legal team and a long-time Republican strategist, said of Mr Trump's reaction to Mr McCain's death. "Our hearts and prayers are with you!" I also direct that the flag shall be flown at half-staff for the same period at all United States embassies, legations, consular offices, and other facilities overseas, including all military facilities and naval vessels and stations.