A motorcade with McCain's casket leaves Thursday morning from the Arizona Capitol, where McCain has been lying in state so thousands of people could say goodbye. John McCain during a viewing at the Arizona Capitol on Wednesday, Aug. 29, 2018, in Phoenix.
Biden, a Democrat who was among the fast friends the Republican senator made across the aisle, said he thought of McCain as a brother, "with a lot of family fights".
McCain is scheduled to lie in state the U.S. Capitol on Friday before a memorial service Saturday at the Washington National Cathedral, where former Presidents George W. Bush and Barack Obama are scheduled to deliver eulogies.
People carrying campaign style placards with the word "McCain" and holding USA flags lined part of the part of the 8-mile (13-kilometer) route the motorcade was taking Thursday to the North Phoenix Baptist Church.
"On behalf of a grateful nation, we will ever remember that John McCain served his country and John McCain served his country honorably'". Both men bested McCain in separate presidential bids.
"I'm confident his legacy of devotion will inspire people around the world", Fitzgerald said.
Meanwhile, the church's senior pastor, Noe Garcia, said Mr McCain was "a true American hero".
On Saturday, McCain's procession will pause by the Vietnam Memorial and head for Washington National Cathedral for a formal funeral service.
The former US presidents joked about McCain's imperfections, while saying he made them better leaders.
Meghan McCain has rebuked Trump, who has a long history of mocking her father.
An honor guard of soldiers, sailors, airmen and Marines carried McCain's flag-draped casket up the Capitol's East steps about 10:45 a.m., as heavy rain fell.
The late Sen. John McCain (R-AZ) was remembered by family and friends at his memorial service at North Phoenix Baptist Church Thursday. "That took my son Beau's life - is brutal, relentless, unforgiving", Biden said.
Throughout the brief ceremony, McCain's widow Cindy, his children, grandchildren and his 106-year-old mother, Roberta, said stalwart facing his casket.
The music chosen for the recession was 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. There his wife, Cindy McCain, laid a wreath to honor those who died in the war.
The Capitol was then opened to the public in the afternoon, allowing visitors to walk past the closed casket after waiting in line outside in temperatures that reached 104 degrees (40 Celsius). McCain wasn't one for conspiracy theories; he was generally courteous and respectful of the press - and, mostly, he truly believed in the system of governance the Founders set up.
"As an army veteran, an army warrant officer for 20-plus years, serving my country, I would be remiss if I didn't show up to honour who we call our maverick", Dr Joseph said. John McCain today in Phoenix, Arizona, and described the meaningful friendship that was formed between the two men who came form very different worlds.
The memorial was laced with humor and featured a racially and ethnically diverse roster of speakers and other participants.
"John McCain, through forgiveness, accomplished what we were unable to do with all our weapons of war", CBS News' Bob Schieffer said.