Arizona Gov. Doug Ducey called McCain "an American hero" who always put his country before himself.
His family had previously said he had ended medical treatment for the condition, revealing that "the progress of disease and the inexorable advance of age render their verdict".
McCain spent the past year undergoing cancer treatment, but his family said Friday that he would discontinue that treatment.
On Saturday night, a black hearse accompanied by a police motorcade could be seen driving away from the ranch near Sedona, Arizona, where the Republican senator spent his final weeks. They tortured and beat him, but McCain refused an early release, denying communist North Vietnam a propaganda victory, and followed a code of conduct that POWs must be released in the order they were captured.
He missed a White House ceremony on December 12, 2017, in which President Donald Trump signed the annual defense bill into law - one of McCain's signature achievements.
"There is no reason for me to hold a grudge or anger", McCain said.
"McCain will be missed by all of us very much", wrote the Defense Minister.
The bad blood between the two men was so thick that it was made known, even before McCain's passing, that Trump would not be invited to his funeral.
The exchange captured the honesty that was a hallmark of McCain, a Navy pilot who was almost killed when his plane was shot down over Hanoi in 1967 and who spent the next six years as a prisoner of war in North Vietnam.
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McCain walks inside the Hoa Lo prison, nicknamed "the Hanoi Hilton", in Vietnam, where McCain was kept as a prisoner of war from October 1967 until March 1973. He went on to win a seat in the House and in 1986, the Senate, where he served for the rest of his life.
After his speech, we presented Senator McCain with the most Australian of gifts, an Akubra hat.
Just minutes after news of the death of Senator John McCain broke Saturday, tributes began pouring in from loved ones, longtime allies, and former political foes, as many sought to honor the senator who had built a bipartisan reputation over his decades in Congress.
"The spirit that drove him was never extinguished: we are here to commit ourselves to something bigger than ourselves", Mr Biden said.
Senator Chuck Schumer announced that he wants to name the Senate building that housed Mr McCain's suite of offices after the Arizona senator, who served as chairman of the Commerce Committee and the Senate Armed Services Committee. "When you hear cancer, a nuclear bomb goes off in your life".
"I said I know, and I mean this sincerely, I know if I picked up the phone tonight, and called John McCain and said, 'I need your help, come, ' he'd get on a plane and come".
Cindy McCain, the senator's wife, wrote in a tweet, "I love my husband with all of my heart".
The senator is survived by his mother, Roberta; his wife, Cindy; two sons and a daughter from a first marriage, Douglas, Andrew and Sidney; four children from his second marriage, Meghan McCain, Jimmy McCain, Jack McCain and Bridget McCain; a brother, Joseph McCain; a sister, Jean McCain Morgan; and five grandchildren. I am so lucky to have lived the adventure of loving this incredible man for 38 years. "He passed the way he lived, on his own terms, surrounded by the people he loved, in the place he loved best".
During a recent appearance by former Vice President Joe Biden, who is promoting his new book, "Promise Me, Dad: A Year of Hope, Hardship and goal", the Democrat lauded Meghan's father and offered words of encouragement. "We honour his lifetime of service to this nation in our military and in public life".