They weren't expected to produce a final deal but optimism about progress had buoyed global stock markets this week.
US President Donald Trump boasted Tuesday that US-China trade negotiations were going "very well" as officials held talks in Beijing that will spill into a third day. For its part, China said the meetings were " extensive, in-depth and detailed", and laid the foundation for a resolution of the conflict.
However, headwinds remain, chief among them the development of trade talks between Washington and Beijing.
Some analysts say that China - Pyongyang's key diplomatic ally and main source of trade - could use Kim's visit as a bargaining chip in the U.S. trade talks.
Investors welcomed signs of optimism from the talks. Hong Kong's main market index rose 2.3 percent while Tokyo was up 1.3 percent.
United States companies also want action on Chinese policies they complain improperly favor local companies.
"Asian stocks jumped after trade talks were extended for an unscheduled third day, fueling hopes that the world's two largest economies may soon reach a trade deal, putting an end to months of tariffs on each other's goods", reports NPR's Shanghai-based correspondent Rob Schmitz.
President Donald Trump and President Xi Jinping have given their officials until March 1 to reach an accord on "structural changes" to China's economy on issues such as the forced transfer of American technology, intellectual-property rights, and non-tariff barriers.
"If the results of the talks are positive, it would be beneficial for both China and the U.S. and also a good news for the global economy", he added. -China Business Council, which represents American companies that do business with China.
On Wednesday, a clutch of Fed officials said they would be cautious about any further increases in interest rates so the central bank could assess growing risks to an otherwise-solid US economic outlook.
The truce came after the two sides imposed import duties on more than $300 billion of each other's goods.
In another sign of subsiding worries about the United States economic outlook, Fed funds rate futures show traders are now pricing in a small chance of a rate hike in 2019, a change from late last week when futures markets had priced in a cut by the end of the year.
People familiar with the U.S.
People familiar with the discussions said positions were closer on areas including energy and agriculture but further apart on harder issues.
Speaking at a daily news briefing in Beijing, Chinese foreign ministry spokesman Lu Kang confirmed both sides had agreed to extend the talks beyond Monday and Tuesday as originally scheduled.
Vice Commerce Minister Wang Shouwen headed the vice ministerial level talks for China, though Vice Premier Liu He, a top economic adviser to Xi, made an appearance at a meeting on Monday. Prior to the meeting, China made a number of concessions to USA demands including temporarily cutting punitive tariffs on US -made cars, resuming soybean purchases, promising to open up its markets for more foreign investment, and drafting a law to prevent forced technology transfers.
On Monday, Chinese importers made another large purchase of USA soybeans, their third in the past month. US government data shows the Asian nation scooped up more than 2.6 million metric tons of beans in December and at least another 1.3 million were sold this year, according to people familiar with the matter.
The OPEC-led cuts are aimed at reining in an emerging supply overhang, in part because USA crude oil output surged by around two million barrels per day in 2018, to a record 11.7 million bpd.
The talks that started Monday were the first face-to-face meetings since Mr. Trump and his Chinese counterpart, Xi Jinping, agreed on December 1 to suspend further action against each other's imports for 90 days while they negotiate over USA complaints that Beijing steals or pressures companies to hand over technology. Trump tweeted "Talks with China are going very well!" late on Tuesday in Beijing.