Trump said in a radio interview with WMAL in Washington that "people have to be careful because at some point I fight back." The president added "I'm being very, very nice but at some point I fight back and it won't be pretty."
McCain's answer a short time later was simply: "I have faced tougher adversaries."
In Philadelphia on Monday night, the six-term Republican senator from Arizona received an award for a lifetime of service and sacrifice to the country. In addition to recalling his more than two decades of Navy service and his imprisonment in a Vietnam prisoner of war camp, McCain took a moment to go a step further than the night's other speakers, who lamented what many described as a fractured political climate.
"To abandon the ideals we have advanced around the globe, to refuse the obligations of international leadership for the sake of some half-baked, spurious nationalism cooked up by people who would rather find scapegoats than solve problems," he said, "is as unpatriotic as an attachment to any other tired dogma of the past that Americans consigned to the ash heap of history."
He continued: "We live in a land made of ideals, not blood and soil."
McCain, who is battling brain cancer, told reporters Tuesday morning that he has had tougher fights, and then smiled.
Trump said in the radio interview that McCain voted against Republican efforts to dismantle Barack Obama's Affordable Care Act. He says the vote was a "shocker."
McCain and Trump have long been at odds. During the campaign, Trump suggested McCain was not a war hero because he was captured in Vietnam.