Top officials from the world's two biggest economies held a second day of trade talks Tuesday at the UK's historic Lancaster House, with meetings stretching into the night.

All eyes are on the outcomes as both sides try to overcome an impasse over export restrictions, with US officials earlier accusing Beijing of slow-walking approvals for shipments of rare earths.

Bessent left the meetings early to return to Washington for testimony before Congress, a US official told AFP.

But US Commerce Secretary Howard Lutnick and trade envoy Jamieson Greer, who were also part of the delegation, would further talks as needed with Chinese counterparts, the offical said.

Earlier Tuesday, Lutnick told Bloomberg Television that the negotiations were "going well".

Global stock markets were on edge, although Wall Street's major indexes climbed on hopes for progress.

With meetings dragging on, "the lack of positive headlines weighed on stocks," said Kathleen Brooks, research director at XTB trading platform.

US President Donald Trump told reporters Monday: "We are doing well with China. China's not easy."

The London negotiations follow talks in Geneva last month, which saw a temporary agreement to lower tariffs.

This time, China's exports of rare earth minerals -- used in a range of things including smartphones, electric vehicle batteries and green technology -- are expected to dominate the agenda.

"In Geneva, we had agreed to lower tariffs on them, and they had agreed to release the magnets and rare earths that we need throughout the economy," Trump's top economic adviser, Kevin Hassett, told CNBC on Monday.

Even though Beijing was releasing some supplies, "it was going a lot slower than some companies believed was optimal", he added.

"Our expectation is that after the handshake, any export controls from the US will be eased, and the rare earths will be released in volume," Hassett said.

- 'Mirror arsenal' -

Both countries "have developed almost a mirror arsenal of trade and investment weapons that they can aim at each other," said Emily Benson, head of strategy at Minerva Technology Futures.

As they tap economic tools to try and shift global power structures, she told AFP, it may not be reasonable to expect a typical trade and investment deal from talks.

But both sides could find ways to level off a downward spiral.

Tensions between Washington and Beijing have heightened since Trump took office in January, with the countries engaging in a tariffs war.

The Geneva pact temporarily brought new US tariffs on Chinese goods down from 145 percent to 30 percent, and Chinese countermeasures from 125 percent to 10 percent.

But Trump later said China had "totally violated" the deal.

A dialing-down of temperatures could involve Chinese efforts to shore up some export control licenses caught in their system, Benson said. She noted Beijing appeared understaffed given the volume of requests.

On the US side, this could look like a relaxation of certain export curbs in the high-tech domain, she added.

But observers remain cautious.

"We doubt that the US will back off completely. That's likely to restrain any relief rally," said Thomas Mathews, head analyst of Asia Pacific markets for Capital Economics.

Since returning to office, Trump has slapped a 10 percent levy on friend and foe, threatening steeper rates on dozens of economies.

His tariffs have dented trade, with Beijing data showing Chinese exports to the United States plunged in May.

The World Bank on Tuesday joined other international organizations to slash its 2025 global growth forecast amid trade uncertainty.

Meanwhile, China is in talks with partners including Japan and South Korea to try to build a united front countering Trump's tariffs.

Chinese Vice Premier He Lifeng is heading the team in London, which includes Commerce Minister Wang Wentao and China International Trade Representative Li Chenggang.

Bessent, Lutnick and Greer are leading the American delegation.