"We noted the efforts made in the last 20 years has not succeeded in curbing the threats posed by North Korea's illegal nuclear weapons programmes," Tillerson, who is on his first official visit to China, said after talks with his Chinese Foreign Minister Wang Yi here.
During his visit to South Korea yesterday, Tillerson had cautioned North Korea that all options are on the table to deal with Pyongyang's provocative actions.
"North Korea is behaving very badly. They have been 'playing' the United States for years. China has done little to help," Trump's tweet said.
Both Tillerson and Wang avoided direct response to Trump's tweet.
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"We renewed our determination to work together to convince the North Korean government to choose a better path and different future for its people," Tillerson said.
He said Wang has agreed to work together with the US to see whether "we can bring the government in Pyongyang to a place where they want to make difference and a make course correction and move away from their development of nuclear weapons".
Tillerson affirmed China and the US' commitment to prevent further escalation of tension in the region.
He said issues related to the disputed South China Sea where Trump administration has criticised Beijing's island building were also discussed.
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After his talks with Wang, Tillerson met Chinese top diplomat State Councillor Yang Jiechi whose rank is higher than that of Foreign Minister
Tillerson is due to meet Chinese President Xi Jinping tomorrow.
Though his visit is overshadowed by the North Korean crisis, Tillerson and Wang discussed a broad agenda and arrangements for the first summit meeting between Trump and Xi due to be held in Florida next month.
"The most important principle we have identified is that no matter what happens we have to stay committed to diplomatic means as a way to seek peaceful settlement," he said.
Stating that the main problem in the Korean Peninsula is the conflict between the US and North Korea, he said right now the situation on the peninsula has arrived at "new cross roads".
All parties, including the US, should view the situation in a cool headed and compressive fashion and arrive at a wise decision, he said.