Speaking to reporters from his private golf club in Bedminster, N.J., Trump stood by his threats from earlier in the week.
"Frankly, the people who were questioning that statement, was it too tough? Maybe it wasn't tough enough," he said. North Korea has "been doing this to our country for a long time, for many years, and it's about time that somebody stuck up for the people of this country and for the people of other countries. So if anything, maybe that statement wasn't tough enough.
"And we're backed 100 percent by our military, we're back by everybody and we're backed by many other leaders. And I noticed that many senators and others came out today very much in favor of what I said. But if anything, that statement may not be tough enough."
When asked what's tougher than "fire and fury," Trump responded: "You'll see. You'll see." He added that he would not discuss a possibility of a pre-emptive strike with reporters.
When asked if China could more regarding North Korea's threats, Trump said he thought they "can do a lot more."
"I think China will do a lot more. Look, we have trade with China. We lose hundreds of billions of dollars a year on trade with China. They know how I feel. It's not going to continue like that. But if China helps us, I feel a lot differently toward trade, a lot differently toward trade.
"So we will do - the people of our country are safe. Our allies are safe. And I will tell you this: North Korea better get their act together or they're going to be in trouble like few nations ever have been in trouble in this world."
The new remarks are the latest in a series of back-and-forth threats between the two countries.
On Tuesday, Trump warned North Korea not to make any more threats against the United States. In July, North Korea said it would "strike a merciless blow" at the United States if Washington ever attempted to remove leader Kim Jong Un from power.
"They will be met with fire and fury like the world has never seen," Trump said. "[Kim] has been very threatening beyond a normal state and as I said they will be met with fire and fury and frankly power the likes of which this world has never seen before."
Trump's statement came hours after a U.S. intelligence analysis determined North Korea has made a nuclear warhead small enough to fit on a missile.
By Tuesday evening -- Wednesday morning North Korea time -- Pyongyang began making threats against the U.S. territory of Guam.
A spokesman for North Korea's military told state-run KCNA that it is "now carefully examining the operational plan for making an developing fire at the areas around Guam with medium-to-long-range strategic ballistic rocket Hwasong-12."
Guam is home to Anderson Air Force Base, from which two U.S. B-1B bombers deployed on a mission with the South Korean and Japanese air forces on Monday. The aircraft flew over Japanese airspace before passing over the Korean Peninsula.
North Korea's threat cited the mission, calling for a potential strike on "Anderson Air Force Base in which the U.S. strategic bombers, which get on the nerves of [North Korea] and threaten and blackmail it through their frequent visits to the sky above South Korea, are stationed and to send a serious warning signal to the U.S."
Gen. Kim Rak Gyom, commander of the Strategic Force of the Korean People's Army, issued another statement Thursday morning saying "only absolute force" will work against someone "bereft of reason" like Trump.
The statement, published by state-run Korean Central News Agency says North Korea is "about to take" military action near the U.S. territory of Guam and a plan to do so would be finalized by mid-August.
On Tuesday, North Korea said it would take "physical action" in reaction to new U.N. sanctions.
"Packs of wolves are coming in attack to strangle a nation," a statement from Pyongyang carried by KCNA said. "They should be mindful that [North Korea's] strategic steps accompanied by physical action will be taken mercilessly with the mobilization of all its national strength."
In his Thursday comments, Trump said the United States will "always consider negotiations" but that the two countries have been negotiating for 25 years.
"What they've been doing, what they've been getting away with, is a tragedy and it can't be allowed," he said.