The school choir from Brophy College Preparatory in Phoenix - where McCain's sons Jack and Jimmy attended - performed a rendition of "Amazing Grace" early in the memorial.
Those in Arizona who knew, respected, watched and loved Sen.
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Meanwhile, the church's senior pastor, Noe Garcia, said Mr McCain was "a true American hero".
McCain "could not stand the abuse of power wherever he saw it, in whatever form, in whatever country", Biden said.
"Things have changed so much in America, they look at him as if John came from another age because he lived by a different code, an ancient, antiquated code where honor, courage, character, integrity, duty mattered", Biden said, alluding to politics in the Age of Trump, of which McCain had frequently and vocally condemned. Drawing on the tragedies suffered in his own life - the deaths of his first wife and daughter in a auto accident in 1972, and his son Beau from cancer in 2015 - Biden offered consolation to McCain's family, calling his absence "all-consuming".
The motorcade was expected to pause at the Vietnam Veterans Memorial where McCain's wife, Cindy, will lay a ceremonial wreath to honor those whose lives were lost during the Vietnam War.
Arizona Cardinals wide receiver Larry Fitzgerald Jr. - who became friends with McCain after his National Football League career began, and who recently wrote a piece for Sports Illustrated on his admiration for McCain's service in Vietnam - is also slated to give remarks.
The recessional music will be Frank Sinatra's signature song, "My Way", paying tribute to a man who became known for following his own path based on his personal principles.
McCain stood out during the last two years as a key rival and critic of U.S. President Donald Trump, a fellow Republican whom McCain's family has asked not to attend the funeral.
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The ceremony was the first of two days of services in Washington honoring the Arizona senator, who served in Congress for 35 years.
A military aircraft will take McCain to Washington, D.C., for a public viewing in the U.S. Capitol Friday and a service at the Washington National Cathedral Saturday. The motorcade carrying his American flag-draped casket arrived just before 10 a.m.
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.
Biden, quoting the Declaration of Independence, said, "We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable rights".
McCain's family, friends, congressional colleagues and staff, as well as US and worldwide leaders, were invited to attend and participate in the service. McCain's widow pressed her face against her husband's coffin, and daughter Meghan McCain erupted in sobs.
Arizona is paying a final tribute Thursday to the late Sen.
Arizonans began lining the streets and mourners gathered at a Baptist church Thursday for a second day of memorial services for Sen.
Ahead of the service Thursday morning, the line for people with tickets to sit in the public section wrapped halfway around the block-sized church. His fight: "legendary. But what made Senator McCain so special was he cared about the substance of my heart rather than where I came from".
Biden, who got to know McCain when he served as a Navy liason for the Senate, recalled traveling around the world with the future Arizona senator in the 1970s as part of his duties on the Senate Foreign Relations Committee.
"John's absence is all-consuming", Biden said.