Traditionally, presidents issue a proclamation to extend the period of time where the flags are flown at half-staff after the death of a member of Congress.
While Trump and McCain had an infamously contentious relationship - including the time when the then-presidential candidate mocked the Arizona Republican for getting captured while fighting in the Vietnam War - the president did not bury the hatchet after McCain's passing. The White House offered no official statement, but Trump did tweet his "deepest sympathies and respect" to McCain's family.
The White House did not immediately respond to a request for comment.
Just after midnight on Sunday night, the flag flying above the White House was hoisted back to full staff.
Trump shared a sympathetic message across social media platforms, stating "our hearts and prayers are with you", however alongside the message on Instagram was an image of himself. Plans call for McCain, a former Navy pilot, to be buried Sunday in the cemetery on the grounds of the U.S. Naval Academy in Annapolis.
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McCain was held captive as a prisoner of war in Vietnam for more than five years, and spoke out on behalf of the military and veterans throughout his life.
McCain said the battles in Vietnam prepared him for high office.
Flags remained at half staff along the National Mall, around the Washington Monument and at the Capitol on Monday to honor McCain, a frequent critic of President Donald Trump. McCain served in the chamber for six terms, most recently as chairman of the Armed Services Committee.
A private burial service next Sunday will conclude almost a week of events honouring the Navy aviator, prisoner of war, congressman, long-time senator and presidential contender.
McCain will lie in state in the Capitol Rotunda on Friday.