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Senator John McCain of Arizona called on Donald J. Trump to make amends to veterans for his belittling comments about prisoners of war and suggested he would be unlikely to appear on a stage with Mr. Trump until that happened.

Mr. McCain has committed to supporting Mr. Trump as the Republican nominee for president. But in an interview that aired on CNN’s “State of the Union” on Sunday, Mr. McCain expressed deep dismay at the tenor of the Republican presidential race, saying Mr. Trump should make amends to “a body of American heroes” he had offended.

Mr. Trump mocked Mr. McCain last summer for having been captured and imprisoned during the Vietnam War, saying that he preferred “people who weren’t captured.”

Mr. McCain, who was the Republican presidential nominee in 2008, told CNN that he was personally indifferent to Mr. Trump’s ridicule but that he could not abide the affront to veterans in general. Asked if he would appear on the campaign trail with Mr. Trump, Mr. McCain said “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,” Mr. McCain said. “When he said, ‘I don’t like people who were captured,’ then there’s a body of American heroes that I’d like to see him retract that statement — not about me, but about the others.”

Mr. McCain’s comments add to the already extraordinary pressure on Mr. Trump to mend his relationships across the Republican Party and win over a range of party leaders he has alienated in the 2016 campaign. One of Mr. McCain’s closest friends in the Senate, Lindsey Graham of South Carolina, has already announced that he will not vote for Mr. Trump under any circumstances.

Mr. McCain said it was incumbent on Mr. Trump to “heal many of the wounds” from the primary season. The senator said the “personalization” of the 2016 race was like nothing he had ever seen, “where people’s integrity and character are questioned.”

Noting the rift that had opened in the Republican Party, Mr. McCain said the party’s leaders had lost touch with many voters in Mr. Trump’s constituency — mainly, he said, older, white, blue-collar workers who see no job prospects.

“There is some distance, if not a disconnect, between party leadership and members of Congress,” Mr. McCain said,“and many of the voters who have selected Donald Trump to be the nominee of the party.”