Washington has previously said all options, including military, are on the table in its review of policies toward North Korea and Japanese officials are keen to know more details.
Tillerson began his first Asian visit as secretary of state in Japan on Wednesday and will travel to China on Saturday with a main focus on finding a "new approach" on North Korea after what he described as two decades of failed efforts to denuclearise the insular nation.
On Friday, Chinese Foreign Ministry spokeswoman Hua Chunying reiterated that talks were the best way to resolve the problems of the Korean peninsula.
Wang said he and Tillerson "both hope to find ways to restart the talks".
Trump has been a frequent China critic, and the encounter could be crucial to setting the tone in the big-power relationship.
Chinese officials have said they do not have the influence over North Korea that Washington and others believe, and have expressed fears poverty-struck North Korea could collapse if it were cut off completely, pushing destabilising waves of refugees into northeastern China. Last month, another two South Koreans who help North Korean defectors were arrested in China. Trump said in the tweet.
The language from Tillerson and Wang was notably conciliatory after a run-up in which Trump accused China of doing nothing to control its rogue neighbour, while China accused the USA of fuelling hostilities.More news: Manchester United midfielder Fellaini ends Premier League goal drought
The U.S. policy of "strategic patience," waiting for North Korea to change course or collapse, is ending, Tillerson said.
So how prepared is the U.S.to take on a nuclear threat? "All options are on the table", Tillerson told reporters at a joint press conference with his South Korean counterpart Yun Byung Se. Right now the status-quo is not working.
North Korea is casting a long shadow over this trip, both for its potential nuclear threat and the recent flurry of missiles it tested, in a launch that sent weapons hundreds of miles toward Japan before landing in the Sea of Japan. The ballistic missiles landed inside Japan's exclusive economic zone - an area according to worldwide law that extends 200 kilometers off a country's coastline.
It has continued to defy the worldwide community, even after two rounds of UN-backed sanctions, and last week test fired a salvo of missiles that fell in waters off Japan.
Wang Dong, a North Korea expert at Peking University, said it was wrong to think Beijing can control the unpredictable and head-strong Pyongyang.
The two sides appear to have toned down differences as they work on finalising a trip by Xi Jinping to the USA, possibly next month, for his first summit with Donald Trump.
The US has 28,000 troops stationed in South Korea to defend it from the North, but Seoul is within range of Pyongyang's artillery, and analysts believe any conflict could risk rapid escalation and heavy casualties.