China-US ties are now developing positively and steadily, Wang said, calling for implementation of the consensus reached by Chinese President Xi Jinping and US President Donald Trump.
The paper added that the possession of strong nuclear weapons is "the only way" to ultimately put North Korea-U.S. relations in order and the "absolute collateral" for peace and security that has been threatened by the joint military drills conducted by Washington and South Korea, Yonhap News Agency reported.
Although Tillerson had warned before his visit to China that the U.S. may take pre-emptive military action against North Korea, he refrained from making strong comments during his two-day visit.
He was speaking in South Korea, the second leg of his first visit to Asia since taking office.
"The United States and China are the world's two largest economies, and we must both promote stability and growth". "We should properly handle and manage sensitive issues to promote the healthy and stable development of the Sino-US relationship", said Xi.
Last month, Trump and Xi had a telephone conversation that was described as warm and cordial.
Stephen Orlins, president of National Committee on US-China Relations, said that the positive momentum during Tillerson's visit could lay the foundation for a meeting between Xi and Trump.
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Officials on both sides said North Korea dominated the discussions as two countries believe the situation reached unsafe levels.
One Beijing-based Western diplomat said it was in Xi's interests to be nice to Trump for now as China does not want any distractions or external instability ahead of the Chinese Communist Party congress in the fall.
Asia is on edge following North Korea test-firing four missiles into the Sea of Japan last week, a move seen as a clear provocation of Japan and South Korea.
"We need to make joint efforts to advance the cooperation between China and the USA, and we believe that we can make sure the relationship moves ahead in a constructive fashion in the new era".
The two countries should also enhance coordination on regional hotspot issues, respect each other's core interests and major concerns and encourage friendly exchanges between the two peoples, said Xi.
The nuclear-armed North has test-launched a series of missiles in recent months and conducted two nuclear tests previous year. The two also discussed the groundwork for a forthcoming summit between the two superpowers next month, where President Trump is expected to host President Xi at his Mar-a-Lago resort in Florida.
Xi also extended welcome to President Trump for a visit to China.
The US and China still do not see eye-to-eye on multiple issues, including the One China policy - that denies global recognition to Taiwan as an independent state, political freedom in Hong Kong, and the rights of the country's Tibetan minority.
He said he would work with China to "bring North Korea to a different place where we are hopeful we can begin a dialogue".