Washington (CNN) Former President Barack Obama lauded John McCain's efforts to push the nation to rise above "mean and petty" politics in his tribute Saturday to the Arizona Republican, who served for more than three decades in the Senate.

"So much of our politics, our public life, our public discourse can seem small and mean and petty, trafficking in bombast and insult, and phony controversies, and manufactured outrage. It's a politics that pretends to be brave and tough, but in fact is born of fear," Obama said in a eulogy for McCain at a memorial service at Washington National Cathedral. "John called on us to be bigger than that. He called on us to be better than that."

Obama, who was McCain's rival in the 2008 presidential race, added, "That's perhaps how we honor him best, by recognizing that there are some things bigger than party, or ambition, or money, or fame, or power, that there are some things that are worth risking everything for."

McCain "never hesitated to tell me when he thought I was screwing up, which by his calculation was about once a day," the Democratic former president said, drawing some laughter from the crowd. "But for all our differences, for all of the times we sparred, I never tried to hide, and I think John came to understand, the long-standing admiration that I had for him."

Obama said it was "no secret" that McCain had a temper that was a "force of nature, a wonder to behold."

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