In a televised new year speech, he said the entire US was within range of North Korean nuclear weapons, adding: "This is reality, not a threat."
But he also offered a potential olive branch to South Korea, suggesting he was "open to dialogue".
North Korea may also send a team to the Winter Olympics in Seoul, he said.
When asked by reporters to respond to Mr Kim's latest threats, US President Donald Trump said, "We'll see, we'll see".
He was speaking at the sidelines of New Year's Eve celebrations at his Mar-a-Lago resort in Florida.