Updated 12:47 p.m. | Former President Barack Obama hailed the late Sen. John McCain as “an extraordinary man” who never lost his “zeal for life.”

“A warrior. A statesman. A patriot. Who embodied so much that is best in America,” Obama said, noting the former senator never shied away from letting the occupants of the Oval Office he never captured know when they were, as Obama put it, “screwing up.”

“He made us better presidents. Just as he made the Senate better. Just as he made this country better,” he said.

Obama revealed that, despite McCain’s seemingly daily critiques of his foreign policy, “every so often” his 2008 campaign opponent would come to the White House for a one-on-one Oval Office chat. They talked about “policy and family and the state of our politics,” he said.

Watch: Bush, Obama Eulogize Former Political Rival and Friend, John McCain

“Our disagreements didn’t go away during these private conversations. Those were real and they were often deep,” he said. “But we enjoyed the time we shared away from the bright lights,” noting they “laughed together and learned from each other.”

And in a rebuke of the current era of American politics, and not noting it helped define his own presidency, Obama said he and McCain “never doubted the other man’s sincerity or the other man’s patriotism” because “when all was said and done, we were on the same team – we never doubted we were on the same team.”

Obama, in his usual sweeping prose, urged Americans to follow the late lawmaker and former Navy pilot’s example to pursue causes that are “bigger” than themselves, and to “get in the arena and fight for this country.”

The latter, he said, McCain understood is “demanded of us all” and is not “reserved for the few.”

“That’s perhaps how we honor him best,” Obama said, “To realize some things are … worth risking everything for” and that America is about “principles that are eternal, truths that are abiding – at his best, John showed us what that means. For that, we are all deeply in his debt.”

The 44th president said he felt “sadness and a certain surprise” after McCain phoned him earlier this year to ask him to deliver one of the D.C. eulogies.

[More on John McCain’s Life and Legacy]

“But after our conversation ended, I realized how well it captured some of John’s essential qualities,” describing the late lawmaker as “unpredictable” and a “contrarian.”

“It showed his irreverence, his sense of humor, his mischievous streak,” Obama said as the crowd laughed in unison, including members of the McCain family. “After all, what better way to get a last laugh than to make George and I say nice things about him to a national audience?”

But then Obama turned serious, saying the invitation showed McCain’s “ability to see past differences to see common ground,” noting “on the surface, John and I could not have been more different.”

The late senator criticized Obama on a nearly daily basis, especially on foreign policy matters, after the upstart Illinois Democrat defeated him in the 2008 presidential campaign. The longtime top Republican on the Senate Armed Services Committee often accused Obama of withdrawing the United States from what he saw as its rightful place as the most powerful country — and, therefore, the one that steps in to resolve problems around the globe.

Watch: Meghan McCain’s Loving Tribute, Scathing Rebuke of Trump at Father’s Funeral

One of McCain’s often-uttered lines was the 44th commander in chief was “leading from behind,” even giving Obama a grade of “F” on foreign policy during his final months in office. He predicted Obama and the U.S. would regret his decision to remove all American troops from Iraq; months later, experts say, McCain was proven correct when the Islamic State extremist group began to form and become more lethal in parts of Iraq.

During their 2008 race, McCain stopped a woman at a campaign event who said she couldn’t trust Obama being president because “he’s an Arab.” McCain shook his head and snatched the microphone from her hands, saying: “No ma’am. He’s a decent family man, a citizen that I just happen to have disagreements with on fundamental issues, and that’s what this campaign is all about.”

Obama on Saturday recounted finding out McCain had shut down the woman, saying he was grateful – but I wasn’t surprised.”

“It was John’s instinct. I never saw John treat anyone differently because of their race or their religion or their gender,” he said. “He saw himself as defending America’s character, not just mine.”

And during his concession speech on Election Night, the GOP nominee sent a message to the country after racial tensions were part of the campaign, saying: “I wish Godspeed to the man who was my former opponent and will be my president.”