BEIJING: Chinese President Xi Jinping and US Secretary of State Rex Tillerson pledged in talks on Sunday that the two powers would work to strengthen a relationship that has been unsettled by disputes over North Korea and trade.

Xi met Tillerson in Beijing just hours after nuclear-armed North Korea tested US-China unity anew with a provocative rocket engine test, and with negotiations under way for a potential Xi summit next month with President Donald Trump in the United States.

Xi said told Tillerson that he and Trump had resolved in a phone call last month "to make joint efforts to advance China-US cooperation, and we believe that we can make sure the relationship will move ahead in a constructive fashion in the new era."

"I'm confident that as long as we can do this the relationship can surely move in the right direction," Xi said.

En route to Beijing, Tillerson visited US allies Japan and South Korea where he declared Washington would drop the "failed" approach of strategic patience diplomacy with Pyongyang -- a sharp break with China, which favours careful diplomacy over heated rhetoric.

Relations have also been strained by China's fierce opposition to a US anti-missile defence system being deployed in South Korea, and Trump's Twitter accusation on Friday that China was not doing enough to control its neighbour and historic ally Pyongyang.

Trump also has repeatedly accused China of unfair trade practice.

But Tillerson has made nice while in Beijing.

"We know that through further dialogue we will achieve a greater understanding that will lead to a ... strengthening of the ties between China and the United States and set the tone for our future relationship of cooperation," Tillerson told Xi.

Earlier Sunday, North Korean state media said the isolated regime had tested a powerful engine hailed by leader Kim Jong-Un as a "new birth" for its rocket industry, which experts view as cover for developing intercontinental ballistic missiles.

- Rocket 'rebirth' -

The announcement's timing appeared intended to sour the visit to China by Tillerson, who warned on Saturday after talks with his counterpart Wang Yi tensions on the Korean Peninsula had reached a "dangerous level."

Tillerson and Wang pledged China and the United States would work together toward denuclearising Kim's rogue regime, but did not offer clear details on how.

It was not immediately clear whether Xi and Tillerson discussed North Korea's latest thumb in the eye.

The North's state news agency KCNA said Kim had overseen the rocket engine test and "emphasised that the whole world will soon witness what eventful significance the great victory won today carries" -- a possible veiled warning to Pyongyang's adversaries.

The report hinted the new engine could be used to put a satellite in orbit, but rocket engines are easily re-purposed for missiles.

North Korea is banned by the international community from pursuing nuclear and missile programmes but has defiantly ploughed ahead.

It staged its two latest nuclear tests last year and recently fired off missiles that it described as practice for an attack on US bases in Japan.

"The leader (Kim) noted that the success made in the current test marked a great event of historic significance as it declared a new birth," of North Korea's rocket industry, KCNA said.

The Xi-Tillerson meeting came as delicate negotiations are under way for a Xi-Trump summit, possibly next month in the United States.

Trump has been a frequent China critic, and the summit could be crucial in setting a lasting tone in the relationship between the world's two largest economies.