"Things will happen to them that they never thought possible," said Trump.
The past week has found the two countries engaging in increasingly hostile rhetoric. In a statement released through North Korea's state-run news service Wednesday, the country's military said it was developing a plan to fire missiles at the U.S. territory of Guam.
Trump's "fire and fury" remark on Tuesday followed reports that North Korea produced a nuclear weapon small enough to fit inside a missile.
Trump pushed back against the suggestion that his administration was being inconsistent.
"There are no mixed messages," he said. "Rex was just, you know, stating the view. Look, here's the view: I said it yesterday. I don't have to say it again. I'll tell you this, it may be tougher than I said it, not less. It may very well be tougher than I said it."
Trump was asked Thursday about a statement from North Korea's military — which described the "fire and fury" comment as a "load of nonsense" and called him a "guy bereft of reason."
"They've been doing this to our country for a long time, many years. It's about time that somebody stuck up for the people of this country and for the people of other countries," he responded. "So if anything, maybe that statement wasn't tough enough. And we're backed by 100 percent by our military. And we're backed by many other leaders."
Trump refused to say whether he would consider a pre-emptive strike on North Korea, using the opportunity to criticize the Obama administration for announcing its military plans, but he was more forthcoming about his view of previous presidents' diplomatic efforts.
"They've been negotiating now for 25 years. Look at [Bill] Clinton. He folded on the negotiations. He was weak and ineffective. You look what happened with [George W.] Bush. You look what happened with [Barack] Obama. Obama, he didn't even want to talk about it," Trump said.