McCain, a former Republican nominee for president, died August 25 from brain cancer. "It's unforgiving. And it takes so much from those we love and from the families who love them that in order to survive, we have to remember how they lived, not how they died", Biden said of the cancer.
The senator from Arizona became the 31st person to lie in state in the U.S. Capitol rotunda, according to the Architect of the Capitol website, which says the country's "most eminent citizens" are given the honor.
It suddenly started to pour on an otherwise hot and sultry day as military members somberly carried his casket from a hearse into the Capitol at roughly 10:40 a.m. - only to abruptly taper off as he was carried into the building.
McCain, who served in Congress since 1983 and in the U.S. Senate since 1987. died last Saturday of brain cancer.
A choir from the Jesuit-run Brophy College Preparatory school that two of McCain's sons attended sang "Amazing Grace". "We're all Americans, and we got to get to the point where we can work together as Americans", said Grant Woods, McCain's former chief of staff.
Professional athletes don't often have the opportunity to stand among current and former high-ranking government officials at public memorial services.
He said, "I pray you take some comfort knowing that because you shared John with all of us your whole life, the world now shares with you the ache of John's death". (Sarah Silbiger/CQ Roll Call) Members of the different services were bearers of McCain's casket into the Capitol. "We are here today to honor an American patriot who served a cause greater than himself", Pence said.
Meanwhile, the church's senior pastor, Noe Garcia, said Mr McCain was "a true American hero".
He says McCain "was about the only politician that I have ever known who cared for the people in his country, and he tried his level best to make it a better place in which to live". Drawing on the tragedies suffered in his own life - the deaths of his first wife and daughter in a vehicle accident in 1972, and his son Beau from cancer in 2015 - Biden offered consolation to McCain's family, calling his absence "all-consuming".
Their daughter Meghan McCain, co-host of the television talk show "The View", sobbed openly.
Former U.S. Vice President Joe Biden speaks during a memorial service to celebrate the life of of U.S. Sen.
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At the end of the almost 90-minute ceremony, McCain's casket was wheeled out of the church to "My Way", in tribute to a politician known for following his own path.
Trump, who has mocked McCain for being captured during the Vietnam War, was asked to stay away from the Capitol service, people close to the White House and the McCain family said.
Also expected to attend were two dozen sitting US senators, Arizona Governor Doug Ducey and his wife, Angela; former Vice President Dan Quayle; and several former senators.
Sen. John McCain's body has arrived to lie in state in the U.S. Capitol rotunda, beginning three days of Washington area memorials that will trace McCain's long career in reverse - from the halls of the Senate to the grounds of the U.S. Naval Academy in Annapolis.
A few firefighters saluted from atop a fire engine parked on an overpass when the 11-vehicle motorcade with a 17-motorcycle police escort passed underneath on Interstate 17.
One man shouted, "We love you!"
After the ceremony at the Capitol on Friday, the public is invited to pay their respects to McCain.
Following the service, McCain's casket was escorted to the Air National Guard base at the Phoenix airport, where it was transferred to a military aircraft bound for Washington, D.C.
Mr Biden made the moving comments during a private memorial service at North Phoenix Baptist Church in Arizona.