President Trump has accused North Korea of "behaving very badly" as he said the country had been "playing" the US for years.
In a tweet posted on Friday Mr Trump added that China has done "little to help!"
Mr Trump's comments come after a warning from American Secretary of State Rex Tillerson that military action by the US will be "on the table" if North Korea elevates its threat level.
During his first trip to Asia since being appointed by Mr Trump, Mr Tillerson said the US policy of strategic patience with Pyongyang had now ended.
Mr Tillerson is using his trip to South Korea, Japan and later China to focus on finding a new approach to North Korea.
It follows what he said had been two decades of failure to stop the rogue state developing nuclear weapons.
"Let me be very clear: the policy of strategic patience has ended," he said.
"We are exploring a new range of security and diplomatic measures. All options are on the table.
"If they elevate the threat of their weapons programme to a level that we believe requires action, that option is on the table."
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Mr Tillerson added that any action by Kim Jong-Un's regime which threatens South Korea will be met with "an appropriate response".
China is being pressed by the US to implement sanctions against North Korea.
And Mr Tillerson says there is no need for China to punish South Korea for deploying an advanced US anti-missile system aimed at defending itself against the North.
The Chinese say the powerful radar in the Terminal High Altitude Area Defence (THAAD) system is a threat to Beijing's security.
Mr Tillerson described Chinese retaliation to the move as "unnecessary and troubling".
"We also believe it is not the way for a regional power to help resolve what is a serious threat for everyone," he said.
"So we hope China will alter its position on punishing South Korea."
North Korea has carried out two nuclear tests and a series of missile launches since the beginning of last year.
Last week it launched four more ballistic missiles and it is believed to working to develop nuclear-tipped missiles that can reach the United States.