Washington (CNN) Former President George W. Bush said whatever rivalry he had with Sen. John McCain "melted away" as they forged a friendship.

"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," Bush said at a memorial service at Washington National Cathedral.

Bush recalled how he and McCain spoke of that "intense period like football players remembering a big game."

"In the process, rivalry melted away," Bush told the crowd of mourners gathered at the cathedral. "In the end, I got to enjoy one of life's great gifts, the friendship of John McCain. And I'll miss it."

Bush said that McCain was "honest, no matter whom it offended," adding that "presidents were not spared."

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