US President Donald Trump launched into a fresh war of words with a fellow Republican on Tuesday, warning John McCain "I fight back, and it won’t be pretty" after the respected senator criticized him in a speech.

Speaking on Monday night at an event held to honor his life’s achievements, McCain accused Trump of spreading a "half-baked, spurious nationalism."

The former presidential candidate and war hero, who was diagnosed with brain cancer in July, added the US must not retreat from global leadership nor "find scapegoats (rather) than solve problems."

Trump lashed out Tuesday, telling conservative radio host Chris Plante: "People have to be careful because at some point I fight back.

"I’m being very nice. I’m being very, very nice. But at some point I fight back, and it won’t be pretty."