Trump said the latest nuclear test by the North - its sixth - showed that "their words and actions continue to be very hostile and dangerous" to the United States.
He also took aim at China - North Korea's biggest trading partner - for failing to exercise its influence to contain Pyongyang's rapidly developing nuclear weapons programme.
Trump previously persuaded China to do more to control the North Korean regime, but Beijing has resisted any pressure saying the issue should be settled through negotiations.
Since then, Trump has appeared less optimistic on Chinese cooperation.
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"North Korea is a rogue nation which has become a great threat and embarrassment to China, which is trying to help but with little success," Trump said today in another tweet.
He indicated that he favours tougher actions against North Korea and the South's preference for talks was not going to yield results. "South Korea is finding, as I have told them, that their talk of appeasement with North Korea will not work, they only understand one thing!" Trump said.
North Korea claimed it has successfully tested a hydrogen bomb meant to be loaded onto an intercontinental ballistic missile. It last carried out a nuclear test in September 2016.
Pyongyang has defied UN sanctions to develop nuclear weapons and to test missiles which could potentially reach the mainland US.
Last month, North Korea threatened to launch missiles to hit the US Pacific territory of Guam after Trump said Pyongyang would face "fire and fury" if it threatened the US. Those threats have not deterred the North's nuclear weapons programme.
Trump and Japanese Prime Minister Shinzo Abe discussed the growing threat from the North Korean actions today. A readout of their conversation, however, did not say whether the phone call - the third between the two leaders in less than a week - happened before or after the North's latest test.
White House Press Secretary Sarah Sanders said the National security team was monitoring the situation. "The president and his national security team will have a meeting to discuss further later today.