Biden's son Beau Biden and another giant of the Senate who both men called a friend, Ted Kennedy, died of the same aggressive tumor.
Trump also maintained in the interview that those saying that he hadn't paid proper respects to McCain were off the mark since he had done so.
The service brought to a close two days of mourning for the US senator and 2008 presidential nominee in his home state.
During his last term in the Senate, in which he has served since 1987, McCain directly challenged the Trump administration and his fellow Republicans on many issues, becoming the deciding vote against the repeal of Obamacare a year ago.
The columnist then invoked Graham's shifting support for Attorney General and former colleague Jeff Sessions.
Family, friends, lawmakers and other guests, including some celebrities, are gathered in the rotunda at the U.S. Capitol, where the body of John McCain lies in state, for a memorial service to honour the six-term senator who lived and worked in the nation's capital for over four decades.
Congress bids a final good-bye, as the nation bows its collective head in memory of John McCain.
The program was choreographed to send a wider message. Mr. Trump's early response to McCain's death on Saturday was criticized.
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President Donald Trump said Thursday that civilian employees of the federal government will not receive raises in 2019. That's wrong - and it disrespects the important work done throughout our country by federal workers.
After the service, McCain's widow, Cindy, and Sen.
More than one speaker urged politicians in the pews and elsewhere to follow McCain's legacy by rejecting tribalism and forging friendships across the aisle.
And the absence of Trump, whose bitter feud with McCain has wrangled U.S. politics during that time, will serve as a final rebuke of the president, highlighting the clash between a Republican elder statesman and the current president from his own party.
"Tonight more than any night, I hold in my heart nothing but love for this country and for all its citizens, whether they supported me or Senator Obama", McCain said at the time.
"No longer protected by McCain, he seems to have lost that famous McCain courage".
Many others were also in tears as they filed solemnly past the casket, often after waiting for hours outside in the blazing Arizona sun.
Members of Congress and a slew of Washington heavyweights surrounded the family.
"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", Trump said in a statement late Monday after the flag was lowered. Vice-President Mike Pence and congressional leaders of both parties will lay wreaths. Former President George W. Bush and former President Barack Obama are expected to give the eulogy. Former Vice-President Joe Biden and others provided a preview of the tributes to come.
If only because Trump is a sitting Republican president who has spent YEARS criticizing every aspect of his predecessor's record, it is utterly baffling that he can't even say whether McCain, his party's 2008 nominee, would have done a better job. The former aviator who was a prisoner of war for more than five years will be buried Sunday at his college alma mater, the U.S. Naval Academy in nearby Annapolis, Maryland.