Hong Kong (CNN) China urged the United States to take a "cool-headed" approach to escalating tensions with North Korea, calling for a diplomatic solution to North Korea's nuclear and ballistic missile programs.

US Secretary of State Rex Tillerson arrived in the Chinese capital Saturday after issuing the administration's bluntest warning yet to North Korea, saying that no option -- including military action -- is off the table.

For two hours, Tillerson met with his Chinese counterpart Wang Yi, who said the United States should "come back to the right track of a negotiated settlement."

Tillerson said that North Korean tensions had reached a "dangerous level" and said China had agreed to work together to make Pyongyang "change course," though he didn't give further details.

North Korean leader Kim Jong Un oversaw a test of a new type of high-thrust engine, state-run KCNA reported on Sunday.

The test was a "success" and was seen as an event of "historic significance" that could lead to the "new birth" of the country's indigenous rocket industry, KCNA said.

Beijing was Tillerson's final stop on his first official trip to Asia, which included visits to Japan and South Korea. The trip follows a string of North Korean missile launches and comes amid fears it's preparing for another nuclear test.

Beijing is North Korea's only real ally and its main economic benefactor, accounting for 70% of the country's trade

US President Donald Trump has repeatedly called on Beijing to use its leverage over its unpredictable neighbor -- and on Friday again singled out China, tweeting, "North Korea is behaving very badly. They have been 'playing' the United States for years. China has done little to help!"

North Korea is behaving very badly. They have been "playing" the United States for years. China has done little to help! — Donald J. Trump (@realDonaldTrump) March 17, 2017

Sunday, Tillerson plans to meet with Chinese President Xi Jinping, who's expected to meet with Trump next month. Tillerson was expected to raise the prospect of financial penalties on companies and banks that do business in North Korea.

"The Trump administration is banking that threats of US military action in South Korea and tougher sanctions on Chinese entities will intimidate Beijing into changing its policies," said Ashley Townshend, a research fellow at the United States Studies Centre at the University of Sydney.

On the trip, Tillerson has signaled a new approach toward North Korea, saying that Washington's policy of "strategic patience" had ended with efforts over the past 20 years to halt North Korea's nuclear development a failure.

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Beijing irked

Beijing, however, has been irked by calls that it isn't doing enough to lessen tensions in the region.

Wang said China had made an "important contribution" to supporting US engagement with Pyongyang but stressed it was, at its core, an issue between the United States and North Korea.

"Washington and Seoul are trying to shift all the burden of solving the North Korean nuclear issue onto China and include China into their strategy toward Pyongyang," it said .

"But that way, China and North Korea will become enemies, further complicating the conflict. The North Korean nuclear issue is caused by Washington-Pyongyang confrontation, to which China has no obligation to shoulder all the responsibilities."

Wang also said that he hoped Washington would examine its plans to defuse tensions, although Tillerson has already dismissed the proposal that the United States should drop joint military exercises with South Korea as a show of good faith to Pyongyang.

He said Friday that Washington did "not believe that conditions are right to engage in any talks at this time." However, on Saturday Tillerson didn't rule out negotiations altogether.

He said he would work with China to "bring North Korea to a different place where we are hopeful we can begin a dialogue."

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Summit preparations

A North Korean soldier, right, tries to take a photograph through a window while US Secretary of State Rex Tillerson visits the DMZ.

It would be the first meeting between the two men, in what many argue is the most important bilateral relationship in the world.

Despite fiery rhetoric on the campaign trail and prior to his inauguration, Trump and his administration have taken a relatively hands off approach to China so far. Tillerson's visit has the potential to set the tone for the relationship.