Many speakers at the ceremony suggested that even in death, McCain could serve as a role model for a politically fractured nation.
"It's a politics that pretends to be fearless and tough but in fact is born of fear. John called on us to be bigger than that, to be better than that".
The late senator's longtime friend, former Sen.
"The America of John McCain", she said, "is generous and welcoming and bold", further describing the country "confident, resourceful, and secure".
Bush, who defeated McCain for the 2000 Republican presidential nomination, called McCain a "man of deep conviction and a patriot of the highest order" and a "friend whom I'll deeply miss". The animosity between Mr McCain and Mr Trump had been mutual, and they clashed often.
Meghan, one of the late senator's seven children with wife Cindy, largely steered away from politics in her tearful speech.
On Saturday Meghan McCain also noted her father's breeding as son and grandson of admirals, accomplishments across the world and tenderness as a father despite his tribulations.
"He was a great man", Meghan McCain said at the Washington National Cathedral.More news: Apple will show off its 2018 iPhones on September 12
The funeral was attended by several leaders, including former Vice President Joe Biden, who was an honorary pallbearer.
They were set to continue at the nationally televised cathedral ceremony, a who's who of political Washington attended by the likes of dozens of congressional colleagues, Bill and Hillary Clinton, former vice presidents Al Gore and Dick Cheney and former secretaries of state Madeline Albright, John Kerry and Henry Kissinger, who is to address the gathering. His flag-draped casket was escorted by military body bearers up the cathedral steps under gray skies.
It was the last public event in Washington, where McCain lived and worked over four decades, and part of McCain's five-day, cross-country funeral procession.
The private ceremony in Annapolis, Maryland, was as carefully planned as the rest of McCain's farewell tour, which began in Arizona after he died August 25 from brain cancer and stretched to Washington.
John McCain, who died a week ago at the age of 81, has brought together many figures from across the political spectrum. "Some values transcend party".
Given that Trump was not invited, Kushner and Ivanka Trump were the most prominent members of the Trump administration in attendance. McCain, a naval aviator, was shot down during the Vietnam War and spent 5 1/2 years as a prisoner of war. He refused to be released without his men. John McCain, R-Ariz., follows as his casket is carried during the recessional at the end of a memorial service at Washington National Cathedral in Washington, Saturday, Sept. 1, 2018.
"John would be the first to tell you he was not a flawless man, but he dedicated his life to national ideals that are as flawless as men and women have as yet conceived". "But he also made me better", Bush said.
"Back", McCain wrote on the last page of his recent memoir, "where it began".