"I’m here to tell North Korea that our president has drawn a red line," Graham wrote in a Twitter post. "If you keep threatening the American homeland with a nuclear weapon we’re going to destroy your regime."
Kim warned President Donald Trump on Tuesday that he could cancel a planned summit in Singapore due to ongoing US-South Korea military drills.
On Wednesday, another warning came from North Korea when the country's nuclear negotiator Kim Gye Gwan said he would walk out of the talks if his country doesn’t get its way.
The United States and South Korea launched a two-week annual air combat exercise on May 11. About 100 aircraft, including US F-22 Raptor stealth fighter aircraft, are participating in the drills, which will last until May 25.