The escalation in rhetoric by Trump - which some US leaders and allies have criticized - comes as North Korea has stepped up its threats against the United States, including a potential missile launch landing near the USA territory of Guam.
Japan and South Korea have also vowed a strong reaction if the North were to go through with the plan to attack Guam.
The U.S. and South Korea are due to start joint military exercises from August 21, while Japanese and U.S. military personnel have begun drills on Japan's northern island of Hokkaido that run through August 28. He did not comment on whether the U.S.is considering a pre-emptive strike on North Korea. If carried out, it would be its most provocative missile launch to date.More news: North Korea tensions command equity market activity, induce spike in volatility
Trump has attempted to leverage China, North Korea's only major ally, to apply more economic pressure on the isolated regime.
"He has been very threatening, beyond a normal statement", Trump said of Kim on Tuesday, in comments that were reportedly off the cuff. "He does something in Guam, it will be an event the likes of which nobody's seen before, what will happen in North Korea", Trump told reporters from the steps of his golf resort in Bedminster, N.J., on Thursday. "If anything, maybe that statement [about "fire and fury"] wasn't tough enough", Trump said Thursday.
"North Korea best not make any more threats to the United States".
Asked if the United States was ready if North Korea made a hostile act, he said: "We are ready".