For more on the late senator’s legacy, tune in to “John McCain: For Whom the Bell Tolls” Saturday at 9 p.m. ET/PT.

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.”

“John was, above all, a man with a code. He lived by a set of public virtues that brought strength and purpose to his life and to his country,” Bush said.

He recognized McCain’s disdain for the abuse of power and instinct to “stand up for the little guy.”

“Those in political power were not exempt. At various points throughout his long career, John confronted policies and practices that he believed were unworthy of his country,” Bush said. “To the face of those in authority, John McCain would insist: We are better than this. America is better than this. “

Bush and former President Barack Obama, McCain’s former rival in the 2008 presidential race, were both asked to deliver eulogies for the Arizona Republican.

McCain died at the age of 81 last Saturday shortly after ending treatment for glioblastoma, an aggressive brain tumor. He was honored at a memorial service on Thursday held at the Arizona state Capitol. On Friday, the senator lay in state in the US Capitol, the 31st person to be given the honor.

A private service will take place at the US Naval Academy in Annapolis, Maryland, on Sunday, and McCain will be laid to rest in the US Naval Academy Cemetery.