Both the US and China spoke of progress Saturday after telephone talks between their leaders over a trade war that has rattled global markets.

"Just had a long and very good call with President Xi of China," US President Donald Trump said on Twitter after his chat with China's President Xi Jinping.

"Deal is moving along very well. If made, it will be very comprehensive, covering all subjects, areas and points of dispute. Big progress being made!"

For his part, Xi told Trump that China places "great importance" on improving bilateral ties and "encourages and supports further talks between the United States and the Democratic people's Republic of (North) Korea, and hopes for positive results," state-run news agency Xinhua reported.

Washington and Beijing imposed tit-for-tat tariffs on more than $300 billion worth of goods in total two-way trade earlier this year, locking them in a conflict that has begun to eat into profits and contributed to stock market plunges.

The leaders of both the United States and China want "stable progress" in ties, Xi said during the call, according to the state Xinhua news agency.

While investors have worried over the trade war between the world's two biggest economies, relations have thawed since Xi and Trump struck a 90-day trade truce in early December while the two sides work to ease tensions by March 1.

Xinhua quoted Xi as saying China and the US are working to implement the terms of that truce.

During the call, Xi expressed hope that "both teams can meet each other halfway and reach an agreement beneficial to both countries and the world as early as possible," according to Xinhua.

Relations between the world's top two economies are "now in a vital stage," Xinhua quoted Xi as saying.

"China attaches great importance to the development of bilateral relations and appreciates the willingness of the US side to develop cooperative and constructive bilateral relations."

The US-China trade war has been among factors pressuring US and global markets in December, alongside worries over slowing growth, a partial US government shutdown, higher US Federal Reserve interest rates and Trump's attacks on the central bank.

Treasury Secretary Steven Mnuchin last Sunday aimed to allay investor anxiety by announcing that he had held a conference call with major bank CEOs, but the comments were widely criticized by market watchers for raising new doubts.

Prior to Saturday's call, there had been small signs of progress -- and the absence of new threats from Trump.

China's customs administration announced Friday it had approved US rice imports, after Beijing's major state-owned grain stockpiler said it had resumed buying US soybeans, and China announced it would suspend extra tariffs added to US-made cars and auto parts starting January 1.

China is also targeting intellectual property theft in the country -- one of the main sticking points in the dispute with the US.

Trump initiated the trade war because of complaints over unfair Chinese trade practices -- concerns shared by the European Union, Japan and others.

Trump is seeking a massive reduction in the US trade deficit with China and deeper reforms to open the economy to foreign companies.

Trade negotiators from China and the United States are planning to meet in January for talks, Beijing said on Thursday, but stopped short of confirming the exact date or location.

"The Chinese and US economic and trade teams have always maintained close communication," commerce ministry spokesman Gao Feng said at a regular briefing.

Deputy US Trade Representative Jeffrey Gerrish will lead the US team for talks during the week of January 7, Bloomberg reported, citing two people familiar with the matter.

These would be the first face-to-face talks since the truce was agreed by both nation's leaders on the sidelines of the G20 summit meeting in Buenos Aires.

Last week, Beijing's commerce ministry said China and the US "made new progress" on the issues of trade balance and intellectual property during a phone call between officials from the two countries.

Resolving the bruising spat could help shore up confidence in the Chinese economy, which itself is bracing for a slowdown.