At a news conference in Seoul, alongside his South Korean counterpart Yun Byung-se, Tillerson said U.S was exploring the new range of diplomatic, security and economic measures and emphasized that Obama administration's policy of "strategic patience"- that saw tightening of sanctions to try and get North Korea back to negotiations aimed at denuclearization - had ended.
China and the United States have an important opportunity to develop bilateral relations, said Xi during the meeting in the Great Hall of People in the capital Beijing, citing telephone calls with his U.S. counterpart Donald Trump. But Chinese official repeatedly say they do not have the influence over North Korea that Washington and others believe.
"The joint interests of China and the United States far outweigh the differences, and cooperation is the only correct choice for us both", Xi added, in comments carried by China's Foreign Ministry. Tillerson had also criticized China while visiting Japan and South Korea.
He further sounded skeptical about the idea of negotiating a freeze that would leave the North with "significant capabilities" that could threaten the region and U.S. forces.
The US president hosted Japanese Prime Minister Shinzo Abe at the estate in February, courting controversy when they set up an impromptu, al-fresco "situation room" in full view of the resort's guests to deal with news of a North Korean rocket launch. Tillerson's visit is expected to pave the way for their first meeting, as early as next month, at Trump's private club in Mar-a-Lago, Florida.
China has proposed double suspension formula under which US and South Korea should stop aggressive military exercises and North Korea should stop nuclear weapons programme, which drew lukewarm response from Washington.
Said the Chinese President: "We both believe that China-US cooperation henceforth is the direction we are both striving for".
Xi said China expects to reach a consensus with Trump and to boost bilateral, regional, and global ties at all levels and properly address and manage sensitive issues.
But for now, the Trump administration seems capable of keeping any controversies behind closed doors.
A black performer who came to fame during the Jim Crow era, Berry's groundbreaking music was popular across racial lines.
Before Mr Tillerson arrived in Beijing on Saturday, Mr Trump said North Korea was "behaving very badly" and accused China of doing little to resolve the crisis over the North's weapons programmes. Rather than taking the press corps with him on his trip, as is customary, Tillerson has allowed only a single reporter, Erin McPike, from the center-right publication Independent Journal Review.
The two leaders discussed the progress in China-U.S. relations, according to statement from acting U.S. State Department spokesperson Mark Toner.
Despite a long list of potential pitfalls, US Secretary of State Rex Tillerson's visit to China, the first by a senior member of the Trump administration, passed relatively smoothly, although there were no tangible gains to show. But last March 8, China called on North Korea to suspend its nuclear and missile activities.
As Tillerson yesterday wrapped up his visit, Chinese President Xi Jinping (習近平) praised his "active efforts" in making a smooth transition of the US-China relationship to the Trump era.