McCain is to be buried Sunday at his alma mater, the U.S. Naval Academy, next to his best friend from the Class of 1958, Adm.
CNN has previously reported that McCain did not want President Donald Trump to attend his funeral and former Alaska Gov. Sarah Palin, who was McCain's running mate in the 2008 presidential election, was not invitedto any of the memorial services.
John McCain was a decorated veteran who was held for more than five years as a prisoner of war in Vietnam.
Meghan McCain, a co-host of "The View" on ABC, was the first speaker to give tribute to her father.
McCain's previous year in office was marked by his confrontation with President Donald Trump.
McCain's widow Cindy, his seven children and his 106-year-old mother Roberta McCain joined scores of members of Congress, state governors, diplomats and other dignitaries at the somber Rotunda ceremony.
Before the service, McCain's family gathered in front of the U.S. Capitol as military service members carried McCain's casket down the steps to a waiting hearse.
The duo mingled with the crowd, which included political figures from both sides of the aisle.Trump who often criticized McCain, even calling him a "dummy", was not at the service.
"We gather here to mourn the passing of American greatness the real thing, not cheap rhetoric from men who will never come near the sacrifice he gave so willingly, nor the opportunistic appropriation of those who lived lives of comfort and privilege while he suffered and served", she said, her voice raising from tearful to anger.
On Saturday, a motorcade will take McCain's casket past the capital's stately monuments en route to the Vietnam Veterans Memorial, where Cindy McCain will place a wreath at the black, v-shaped granite wall inscribed with the names of more than 58,000 USA soldiers killed in combat.
Bush was McCain's rival in the 2000 presidential race.
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Held as a prisoner until 1973, McCain was tortured by his North Vietnamese captors in a jail that Americans dubbed the "Hanoi Hilton".
Other notable attendees included Republican congressional leaders, House Speaker Paul Ryan and Senate Majority Leader Mitch McConnell.
Inside the cathedral luminaries including comedian Jay Leno, former Secretary of State Madeleine Albright, former Senator Bob Dole and others visited with other leaders while a powerful pipe organ played music in the background.
Republican Sen. Lindsey Graham of SC, a close friend of McCain's, and McCain's children Jimmy and Sidney McCain will take part in the ceremony as well.
The motorcade carrying Sen. President Donald Trump, who pointedly was not invited to any of the events in the three days honoring McCain, had feuded frequently with the senator.
John McCain's procession has made a stop at the Vietnam Veterans Memorial on the way to his service at Washington National Cathedral, and his wife, Cindy, has placed a wreath on the memorial.
"The president asked me to be here, on behalf of a grateful nation, to pay a debt of honor and respect to a man who served our country throughout his life, in uniform and in public office".
Just before McCain's service was set to start, Trump tweeted about the "Fake Dossier, attributing a quote to Dan Bongino, who frequently appears on Fox News".
Her tearful, impassioned tribute opened the memorial service for John McCain at Washington National Cathedral.
McCain, who died at the age of 81 last Saturday after a lengthy battle with brain cancer, was an iconic figure in United States politics. Services will be private.