"You have to listen to people that have chosen the nominee of our Republican Party," the Arizona Senator told CNN.
"I think it would be foolish to ignore them," he said.
In an interview to the network, McCain criticized party leaders who are reluctant to back Trump, saying they are "out of step" with the voters who have chosen the controversial businessman as the presumptive Republican nominee.
He said there is a perception, which is largely reality, that there's gridlock in Washington. "And that's given rise to Trump and Sanders."
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"That's something that we in the Republican Party are going to have to look at very carefully," he said.
"I believe that the Republican Party must maintain its viability as a party. And I am a Teddy Roosevelt/Ronald Reagan Republican. I will do everything that I can to continue to steer the Republican Party along those lines in that direction," he said.
"There's always wounds in spirited political campaigns, but I have never seen the personalization of a campaign like this one, where people's integrity and character are questioned," he said.
McCain, who has said that he would not be attending the Republican Convention in Cleveland, did not rule out appearing with Trump during the latter's election campaign.
"I think a lot of things would have to happen (first). I think it's important for Donald Trump to express his appreciation for veterans, not John McCain, but veterans who were incarcerated as prisoners of war," he said.
Responding to a question on his 2008 presidential campaign, when he lost to Barack Obama, the current president, McCain acknowledged that he did commit some mistakes.