Beijing (CNN) North Korea marked the final day of US Secretary of State Rex Tillerson's Asia visit Sunday by claiming to have tested a new type of rocket engine, underlining the country's defiance of recent calls for calm on the Korean Peninsula.

The test came hours before Tillerson met Chinese President Xi Jinping, the highest-level meeting between an American official and a Chinese leader since US President Donald Trump took power in January.

Xi told Tillerson that there are far more shared interests between the two countries than disputes, emphasizing the need for more communication and coordination on matters involving "regional hotspots," according to a statement released by the Chinese foreign ministry.

On Sunday, North Korean leader Kim Jong Un oversaw the successful test of a high-thrust engine , state-run Korean Central News Agency reported, saying the event had "historic significance" that could lead to the "new birth" of the country's indigenous rocket industry.

Trump said Sunday that he'd "had meetings on North Korea," and without mentioning North Korean leader by name said "He is acting very very badly. I will tell you he is acting very badly."

North Korea tested a new rocket at the Sohae Satellite Launching Ground, in North Pyongan Province on Sunday, March 19, 2017.

Tillerson in Asia

Beijing was Tillerson's final stop on his first official trip to Asia, which also included visits to Japan and South Korea.

The trip followed a string of North Korean missile launches , which escalated tensions on the Korean Peninsula and came amid fears Pyongyang is preparing for another nuclear test.

Despite earlier warning that all options -- including military action -- remained on the table in dealing with Pyongyang, Tillerson refrained from the harsh language that he had used in Tokyo and Seoul upon arriving in Beijing.

Xi and Tillerson leaders met for 30 minutes at the Great Hall of the People, a statement from State Department spokesman Mark Toner said.

The men "agreed there are opportunities for greater cooperation between China and the United States, but acknowledged there are, and will be in the future, differences between the two countries," the statement said.

It added that Tillerson said Trump is "anticipating the two will soon be able to meet face to face for discussions that will chart the course for future US-China relations."

Chinese President Xi Jinping (R) meets with US Secretary of State Rex Tillerson (L) at the Great Hall of the People on March 19, 2017 in Beijing, China.

North Korea's only ally

China is Pyongyang's only major global ally, with bilateral trade accounting for 70% of North Korea's total trade, providing a political and economic lifeline to Kim's increasingly isolated regime.

Trump has repeatedly called on Beijing to use its leverage over its unpredictable neighbor.

He singled out China again Friday, tweeting, "North Korea is behaving very badly. They have been 'playing' the United States for years. China has done little to help!"

After meeting his Chinese counterpart, Foreign Minster Wang Yi, on Saturday, Tillerson stressed "renewed determination" by Beijing and Washington to "work together to convince the North Korean government to choose a better path and a different future for its people," without giving details.

Although neither side brought up the subject publicly, Tillerson had been expected to raise the prospect of financial penalties on Chinese companies and banks that do business with 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 Center 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" over the past 20 years aimed at halting North Korea's nuclear development was a failure.

Between the US and North Korea

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

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

An un-bylined opinion piece Friday in the Global Times, a Chinese state-run tabloid, made a similar point.

"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."

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Wang reiterated the Chinese position that the United States should "come back to the right track of a negotiated settlement."

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

Tillerson said Friday that Washington did "not believe that conditions are right to engage in any talks at this time."

However, he left the door open Saturday, saying he would work with China to "bring North Korea to a different place where we are hopeful we can begin a dialogue."

Trump and Xi to meet?

Tillerson was also in Beijing to iron out the details of a tentative summit between Presidents Trump and Xi in Florida in April.

It would be the first meeting between the two men, whose interactions would affect what many consider the world's most important diplomatic relationship.

The Chinese foreign ministry statement quoted Tillerson as saying that Trump expected the two leaders to meet "as soon as possible" but did not confirm the April summit. Xi also invited Trump to visit China, it added.

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.

Trump has not followed through on campaign threats to label China a currency manipulator or impose steep tariffs on Chinese imports.

He also endorsed the "One China" policy, which has governed delicate relations between the United States, China and Taiwan for decades -- after questioning its legitimacy shortly after his election.