WATCH: Presidents, Washington Elite Bid Farewell To Senator John McCain

WASHINGTON (CBS News) — A memorial service for Sen. John McCain took place in Washington Saturday. Former President George W. Bush and former President Barack Obama gave eulogies at the service at the Washington National Cathedral. Both men defeated McCain in his two campaigns to become president, in 2000 and 2008. President Trump did not attend.

The "maverick" senator was previously honored at a memorial ceremony in his home state of Arizona Thursday, where he was eulogized by friend and luminaries such as former Vice President Joe Biden. Thousands of citizens paid respect as he lay in state at the Arizona Capitol.

Then on Friday, McCain lay in state at the U.S. Capitol Rotunda, where top elected officials paid their respects. Senate Majority Leader Mitch McConnell, House Speaker Paul Ryan and Vice President Mike Pence all gave remarks honoring McCain at a morning ceremony. The public had the opportunity to pay respects on Friday afternoon.

McCain will be buried with military honors following a private service at the U.S. Naval Academy Chapel in Annapolis, Maryland, on Sunday.

Right Rev. Mariann Edgar Budde, the bishop of the Episcopal Diocese of Washington, received McCain's casket with a prayer. The casket was then escorted into the cathedral.

The family processed into the cathedral at around 10:00 a.m.

The motorcade carrying McCain's casket arrived at the Washington National Cathedral shortly before 9:30 a.m.

The McCain family arrived at around 9:40 a.m. McCain's casket was escorted by a military honor guard.

Cindy McCain and McCain's children arrived at the Vietnam Memorial, escorted by Defense Secretary Jim Mattis and White House Chief of Staff John Kelly.

Cindy McCain laid a wreath in front of the memorial with the McCain children looking on. The family then departed for the Washington National Cathedral, where the funeral service is occurring.

McCain regularly visited the Vietnam Memorial quietly and with little fanfare to reflect on the war. The senator also helped to restore relations with Vietnam by visiting the sites of his former captivity in the country.

"John McCain, through forgiveness, accomplished what we were unable to do with all our weapons of war," CBS News' Bob Schieffer said.

McCain's casket was escorted from the Capitol shortly after 8:30 a.m.

More: Sen. John McCain Lies In Rest At U.S. Capitol Rotunda

The motorcade carrying McCain's remains is on its way to the Vietnam Memorial for Cindy McCain and the McCain family to pay respects to the soldiers who died in the Vietnam War.

"CBS This Morning" co-host John Dickerson spoke about McCain's legacy on CBSN this morning. Dickerson covered McCain during the 2000 campaign, when the senator held court with his reporters on his campaign bus nicknamed the "Straight Talk Express."

"It was one rolling conversation," Dickerson said about the discussions McCain had with reporters on the campaign bus.

Dickerson also talked about McCain's capacity to admit to his mistakes. Although he voted against making Martin Luther King Jr.'s birthday as a national holiday in 1983, he later apologized for that position in the 2008 campaign.

"He believed in standards of personal conduct and also institutional conduct," Dickerson said.

On its way from the U.S. Capitol to the Washington National Cathedral, the motorcade carrying McCain's remains is stopping at the Vietnam Memorial. McCain's wife, Cindy, is placing a wreath at the memorial in honor of all who died in the Vietnam War.

McCain served as a fighter pilot in the Vietnam War, and was captured and held as a prisoner of war in Hanoi for five and a half years during the conflict.

McCain's funeral is in many ways a tribute to the senator's belief in the power of bipartisanship.

McCain was eulogized by two of his former rivals for the presidency, Mr. Obama and Mr. Bush.

Former Sen. Joe Lieberman, a Democrat-turned-independent, was Vice President Al Gore's running mate in the 2000 campaign. McCain considered Lieberman as a running mate himself in 2008 before settling on Sarah Palin, who did not attend the service.

Several Democrats who served with McCain in the Senate also had roles in the ceremony, including Biden, Whitehouse, Feingold and Hart.

McCain's funeral, in its very composition, is a call for unity in American politics over common values.

Several members of McCain's family are speaking at his funeral in Washington. The program includes McCain's daughter, Meghan, giving a tribute to her father, his son Jimmy reading a poem, and another daughter, Sidney, reading a Bible passage.

Other speakers include prominent public officials such as Mr. Bush and Mr. Obama, as well as former Sen. Joe Lieberman and former Secretary of State Henry Kissinger. McCain's longtime friend in the Senate, South Carolina Sen. Lindsay Graham, is reading a Bible passage.

The two former presidents will hold in a room before entering the nave together.

Pallbearers include Biden, actor Warren Beatty, former New York City Mayor Michael Bloomberg, Rhode Island Democratic Sen. Sheldon Whitehouse, and former Senators Russ Feingold, Phil Gramm and Gary Hart. Another pallbearer is Russian dissident Vladimir Kara-Murza.

Some interpret the inclusion of Kara-Murza as a posthumous message from McCain to Russian President Vladimir Putin and President Trump. McCain criticized Mr. Trump for being too friendly with Putin amid the investigation into Russian meddling in the 2016 election.

(© 2018 CBS Interactive Inc. All Rights Reserved.)

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