Trump tweeted about McCain after his death Saturday but has passed up several chances to comment publicly on the Arizona senator. "John McCain. We appreciate everything McCain has done for our country".
Near the driveway to his ranch in Sedona, Arizona, a sign read "Sen McCain, thank you for your service".
Mr Biden wrote: "As a prisoner of war, John endured the worst of what human beings can do to one another".
McCain also revealed in his memoirs how prayer sustained him while he was a prisoner of war.
Presidents and lawmakers from both parties honoured Sen. At 10:00am local time, a private, formal ceremony inside the Rotunda of the Arizona State Capitol will take place to honor Senator McCain's life and service to the State of Arizona and the nation. But all of us can aspire to the courage to put the greater good about our own.
Former Senator Bob Dole expressed his sympathy on Twitter Saturday night.
The American flag at the White House was lowered to half-staff on Sunday.
John Russell is a Vietnam veteran who says he too admires John McCain.
He would have turned 82 next week. "This is a rare and distinct occurrence for a truly special man", GOP Gov. Doug Ducey said in a tweet.
McCain's funeral plans were no secret. Under state law, the governor's appointee to serve until the next general election in 2020 must come from the same political party. "He had his office there during his entire time".
"My heart is broken", she wrote.
Mr Trump and Mr McCain were at odds until the end.
Foreign Affairs Minister Vivian Balakrishnan said on Sunday (Aug 26) he was "deeply saddened" to learn about the death of USA senator John McCain.
Tributes were also paid from the other side of the political spectrum. "People don't want less of America - they want more", McCain said in 2012. "He will be greatly missed in Pakistan", the foreign minister said. "It sprang from his belief in democracy and freedom".
He was a fighter pilot during the war in Vietnam and was shot down, seriously injured, and captured by the North Vietnamese.
He was elected to the House of Representatives in 1982 and the Senate in 1986.
"He had a joy about politics and a love for his country that was unmatched", said Sen.
She added: "A man who never sought accolades".