North Korea is seriously "miscalculating" President Donald Trump's potential response to its continued provocations and missile tests, Sen. Lindsey Graham, R-S.C., said Tuesday.

That is likely because previous U.S. presidents have not always made the consequences real.

"Every president before him has said, 'we're not going to allow North Korea to have nuclear weapon,'" Graham told Wolf Blitzer on CNN's "The Situation Room." "Well, they've got nuclear weapons. Every president before President Trump has said, 'we're never going to allow them to hit the homeland with an ICBM with a nuclear weapon on top.' They're about to get a capability."

In North Korea's latest missile firing, conducted early Wednesday Korea time, an intercontinental ballistic missile is believed to have reached an altitude high enough it could reach any American city if fired toward the U.S. mainland.

North Korean neighbor and ally China is key to preventing an all-out American attack on the Hermit Kingdom, Graham said.

"This is a provocative act by North Korea," Graham said. "They're miscalculating President Trump. And he is ready, if necessary, to destroy this regime, to protect America. And I hope the regime understands. If President Trump has to pick between destroying the North Korean regime and the American homeland, he's going to destroy the regime. I hope China understands that also."

Even it it means "hundreds of thousands" of North Koreans are hurt, Graham said he stands with Trump if he decides to retaliate.

"The best outcome is not to have a war," he said. "I don't want a war. He doesn't want a war. But we're not going to let this crazy man in North Korea have the capability to hit the homeland. We're not going to live this way. To our friends in China . . . if you don't help us, we'll take care of it. And us taking care of it means that the war's in your backyard, not ours."