Lindsay Graham Sean Rayford/Getty Images Republican Sen. Lindsey Graham believes the US has military options to take out North Korea's nuclear program, but a strike shouldn't just stop there.

In a Tuesday interview on The Today Show, Graham said the US should not only take out the country's nukes, but "North Korea itself."

"[President Donald Trump] is not going to allow the ability of this madman to have a missile to hit America," Graham said. "If there is going to be a war to stop him, it will be over there. If thousands die, they are going to die there, they're not going to die here."

He added that Trump did not want a war but he would not allow North Korea to obtain a reliable nuclear-tipped ICBM. "The Chinese can stop this," he said.

Graham's statement came just days after North Korea tested another intercontinental ballistic missile which experts believe could have the range to hit most of the United States, with the exception of Florida. Some problems still remain with its reentry vehicle, however, which will require at least a few more tests.

Defense Secretary Jim Mattis told House members in June what a potential war with North Korea would be like.

"I would suggest that we will win. It will be a war more serious in terms of human suffering than anything we've seen since 1953," Mattis said, also noting the danger to the heavily-populated South Korean capital of Seoul: "It will involve the massive shelling of an ally's capital, which is one of the most densely packed cities on earth."

"It would be a war that fundamentally we don't want," Mattis said, but "we would win at great cost."