While honoring the legacy ofSen. John McCainat his national memorial service on Saturday, former presidentsBarack ObamaandGeorge W. Bushshared touching tributes to the six-term senator, whom they both cherished as a friend despite any political differences.

“I am honored to be with you to offer my sympathies and to celebrate a great life,” Bush — who defeated McCain in 2000 during the Republican primary election — remarked at the Washington National Cathedral, before discussing the pair’s long political history together.

“Back in the day he could frustrate me, and I know he’d say the same thing about me. But he also made me better,” he remarked, adding that “in recent years” their “rivalry melted away.”

“We sometimes talked of that intense period like football players remembering a big game. In the process, rivalry melted away. In the end I got to enjoy one of life’s great gifts: the friendship of John McCain. And I’ll miss him,” the former president added.

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Bush also appeared to make a swipe at President Donald Trump, whowas not in attendance at the ceremony,instead tweeting about the NAFTA negotiations (and threatening to cut Canada out of the deal). During the funeral, Trump alsoleft the White House to travel to his golf course,Timereported.

“Perhaps above all, John detested the abuse of power,” he added. “There was something deep inside him that made him stand up for the little guy. To speak for forgotten people in forgotten places.”

Although the president was absent from the occasion, bothIvanka TrumpandJared Kushnerwere on hand at the service.

RELATED VIDEO: ‘He Made Me Better.’ George W. Bush Pays Tribute to Former Rival John McCain

“We talked about policy, and we talked about family, and we talked about the state of our politics. And our disagreements didn’t go away during these private conversations. Those were real, they were often deep. But we enjoyed the time we shared away from the bright lights,” he said.

“We laughed with each other and we learned from each other,” Obama continued, adding that the pair “never doubted” that “when all was said and done we were on the same team.”

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Seemingly making his own veiled reference to President Trump, Obama criticized the state of modern politics.

“So much of our politics, the public life, the public discourse, seems small, and mean, and petty,” he said. “Trafficking in bombast and insult, phony controversies and manufactured outrage. It’s a politics that pretends to be brave and tough, but is instead born of fear. John called on us to be bigger than that, to be better than that.”

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During the service, a sweet moment was also captured on social media of Bush slipping a candy toMichelle Obama.

During the memorial service, the longtime politician’s daughterMeghan McCainalsotook a dig at Trump, as she remarked that “the America of John McCain has no need to be great again because America was always great.”

She also referencedTrump’s previous criticism of McCain.

“We live in an era where we knock down old American heroes for all their imperfections. When no leader wants to admit to fault or failure,” Meghan said, then talking to her father. “You were an exception, and you gave us an ideal to strive for. Look, I know you can see this gathering here in this cathedral. The nation is here to remember you.”

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Reports have varied as to whether the president was invited to Sen. McCain’s funeral. White House sources told the Associated Press that McCain’s family asked Trump not to attend. However, a McCain family source previously told PEOPLE the longtime politiciandid not prohibit Trump from attending his funeral.

“John had a feud with the president, and it got pretty intense, but I never heard anyone in the family say John banned Trump, and he never said that to me,” the source told PEOPLE. “John didn’t ban Trump. John could be spiteful, and he loved a good fight, but he wouldn’t do something like that.”

A second family source added: “I didn’t hear John say it. But I wouldn’t be surprised if John didn’t want Trump there.”

source: people.com