The president said: “They are behaving in a very, very dangerous manner and something will have to be done about it.”
However, Donald Trump moderated his comments, saying: “We’ll just take a look at what happens over the coming weeks and months.”
North Korea tested an intercontinental ballistic missile (ICBM) with the potential to hit Alaska on July 4.
Despite the ICBM’s relatively short flight and eventual crash into the sea, the test has been labeled a sharp military escalation by the US.
“I have pretty severe things that we’re thinking about,” President Trump said of a possible US response.
“That doesn’t mean that we’ll do them.”
President Trump said other nations should challenge North Korea’s “very, very bad behavior”.
He was speaking in Warsaw, Poland, at a joint news conference with the Polish President Andrzej Duda.
President Trump is due to meet with other world leaders at the G20 summit in Germany on July 7.
His comments follow those of US ambassador Nikki Haley, who told the UN Security Council that the US was willing to use its “considerable military forces” on North Korea “if we must”.
The US and South Korea have already stepped up military drills, firing missiles into the Sea of Japan in an apparent show of strength.
North Korea, however, said it would not negotiate over its missile program unless the US ended its “hostile policy” against Pyongyang.
Unless the US stopped its “hostile policy”, North Korea would “never put the nuke and ballistic rocket on the negotiating table”.
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