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.
McCain is an American hero who dedicated his life to his country and that flag at 1600 Pennsylvania Ave.is not Trump's flag.
Mr Trump tweeted about Senator McCain after his death on Saturday but has passed up several chances to comment publicly on the Arizona senator.
After a day of ignoring shouted questions about McCain, Trump broke his silence during a gathering of evangelical leaders at the White House on Monday evening.
The American Legion wrote a letter to Trump, urging for the White House flags to be lowered.
In the statement, released two days after the statesman's death, the USA president said he respects Mr McCain's "service to our country".
Despite this, he had long-running feud with President Donald Trump: the two were often critical of one another, with McCain attacking Trump's leadership and Trump questioning McCain's heroism as a prisoner of war for five years.
Mr Trump has now repeated this honour for Mr McCain, saying this recognised the "longstanding service" he had given.
McCain, meanwhile, remained critical of Trump to the end, calling his policies "half-baked, spurious nationalism cooked up by people who would rather find scapegoats than solve problems".
Graham also said that White House chief of staff John Kelly had reached out to the McCain family and had spoken to Cindy McCain, offering the administration's assistance in whatever she needs.
Senator McCain died Saturday from an aggressive form of brain cancer at age 81.
At the same time, the White House released a statement from the president in which Trump said that, despite differences on policy and politics, he respects McCain's service to the US and ordered flags be flown at half-staff until his internment.
John McCain's funeral on Thursday, Aug. 30, 2018.
McCain will be buried Sunday at his college alma mater, the U.S. Naval Academy in Annapolis, Maryland.
On Friday, McCain is scheduled to lie in state at the Capitol Rotunda, with Senate Majority Leader Mitch McConnell, House Speaker Paul Ryan and Vice President Mike Pence giving remarks at a corresponding ceremony, the site reports.
"John McCain was a true American hero", said French President Emmanuel Macron.
After Trump took office, McCain established himself as a leading critic, opposing Trump's immigration-limiting order, warning him against coziness with Moscow and lecturing him on the illegality of torture. John McCain, it's easy to focus on all that he did - the sacrifice and victories, the wounds of war and the joy in service. "Literally nearly the last thing he said to me was 'I love you".