Arizona Sen. John McCain said Monday that he isn't looking for an apology from Donald Trump, but said Trump owes one to veterans for implying they aren't war heroes if they were captured.

"[H]e might owe an apology to the families of those who have sacrificed in conflict and those who have undergone the prison experience in serving their country," McCain said on MSNBC Monday morning.

"There are so men and some women who served and sacrificed and happened to be held prisoner. To denigrate that service in any way is offensive to veterans," he added.

Over the weekend, Trump said McCain was not a war hero because he was a prisoner of war during the Vietnam War. Trump also said later that "perhaps" McCain is a war hero, but the damage was done.

On Monday morning, Trump refused to apologize for his comment on NBC, and said "I'm not a fan of John McCain. He's doing a horrible job with the vets."

McCain refused to attack Trump personally for his comments, nor for Trump's decision to avoid service during the Vietnam war.

"A great honor of my life was to serve in the company of heroes. I'm not a hero," he said. "For me to look back in anger at anyone is nonproductive. And our country was divided in an almost unprecedented fashion during the Vietnam War, and when I came home I was shocked. So I've worked ever since to try to heal those wounds."

The feud began last week when McCain, a former Republican presidential nominee, suggested Trump's remarks about immigrants "fired up the crazies" at one of his Arizona rallies. Trump then called McCain a "dummy."