During his speech, which came just before former Vice President Joe Biden, Fitzgerald offered some lighthearted comparisons between he and McCain.
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".
"Many people might wonder what a young, African-American kid from Minnesota and a highly-decorated Vietnam War hero-turned-United States senator might have in common".
A light rain fell as McCain's casket was carried into the Capitol by members of America's military services.
McCain, who died Saturday months after announcing that he had been diagnosed with an aggressive brain cancer, was initially honored in the state that he represented in Congress for 35 years.
At the church, a choir from the Jesuit-run Brophy College Preparatory school that two of McCain's sons attended sang "Amazing Grace".
Hours before Arizona Sen. (Sarah Silbiger/CQ Roll Call) Members of the different services were bearers of McCain's casket into the Capitol. He complimented McCain for his loyalty, for his tremendous bond with his family, and his great love for America.
Meanwhile, the church's senior pastor, Noe Garcia, said Mr McCain was "a true American hero".
He looked at me and said: Dan, that is a lie.
McCain took time with newer members of the Senate, to coach them and travel with them, Sullivan said. 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".
Both men were forged in the fires of deep pain - Biden lost his wife and daughter in a auto accident; McCain had just gotten out of Vietnam, where he was tortured at the hands of his captors for 5 1/2 years.
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 based on his personal principles.More news: Canadians under pressure to sign new free trade pact
McCain clashed openly with President Donald Trump, who mocked McCain for getting captured during the Vietnam War.
PHOENIX - Thousands of people paid their respects to U.S. Sen.
The service brought to a close two days of mourning for the six-term senator and 2008 GOP presidential nominee in his home state.
As the hearse made its way along the 8-mile route, people held signs that read simply "McCain" and cars on the other side of the highway stopped or slowed to a crawl in apparent tribute.
Arizona State Troopers escort the motorcade carrying Sen. John McCain, the maverick politician and former prisoner of war who died at 81.
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.
Fitzgerald celebrated McCain as a friend as well as an inspiration, remarking love not only for family and friends but for fellow man in general, irrespective of their race or party.
"Meghan McCain's face says it all", said user Stuguru.
The public began filing into the Capitol to pay their respects to McCain around 1 p.m.
McCain was also good friends with the late Sen.
Michael Fellars was among those awaiting the motorcade outside the church Thursday. It was about a prison guard in Vietnam who showed McCain unexpected kindness by loosening the painful ropes around his wrists and, much later in his imprisonment, drawing a cross in the dirt for him as a sort of Christmas gift.