The gathering of key officials from the world's two biggest economies began Monday in London, after an earlier round of talks in Geneva last month.

Stock markets wavered as investors hoped the talks will bring some much-needed calm on trading floors and ease tensions between the economic superpowers.

A US Treasury spokesman told AFP on Tuesday the "talks resumed earlier this" morning.

One of US President Donald Trump's top advisers said he expected "a big, strong handshake" at the end of the talks in the historic Lancaster House, operated by the UK foreign ministry.

Trump told reporters at the White House on Monday: "We are doing well with China. China's not easy.

"I'm only getting good reports."

The agenda is expected to be dominated by exports of rare earth minerals used in a wide range of things including smartphones, electric vehicle batteries and green technology.

"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.

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

Still, he said he expected "a big, strong handshake" at the end of the talks.

"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 added.

He also said the Trump administration might be willing to ease some recent curbs on tech exports.

- Concessions? -

Tensions between Washington and Beijing have heightened since Trump took office in January, with both countries engaging in a tariffs war hiking duties on each other's exports to three figures -- an effective trade embargo.

The Geneva pact to cool tensions 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 recently said China had "totally violated" the deal.

"Investors are willing to grab on to any positive trade headline right now, as this is keeping hopes of a rally alive," said Kathleen Brooks, research director at trading group XTB.

Ipek Ozkardeskaya, senior analyst at the Swissquote Bank, said that although there had been "no breakthrough" it seemed "the first day of the second round of negotiations reportedly went relatively well".

"Rumours are circulating that the US may be willing to make concessions on tech exports in exchange for China easing restrictions on rare earth metal exports," she said.

Rare earth shipments from China to the US have slowed since the tariff war was triggered by Trump's so-called "Liberation Day" announcements, according to Brooks.

The US leader slapped sweeping levies of 10 percent on friend and foe alike, and threatened steeper rates on dozens of economies.

The tariffs have already had a sharp effect, with official figures from Beijing showing Chinese exports to the United States in May plunged by 12.7 percent.

China is also in talks with other trading partners -- including Japan and South Korea -- to try to build a united front to counter Trump's tariffs.

Chinese leader Xi Jinping on Tuesday urged South Korea's new President Lee Jae-myung to work with Beijing to uphold free trade to ensure "the stability and smooth functioning of global and regional industrial and supply chains."

"A healthy, stable, and continuously deepening China-South Korea relationship aligns with the trend of the times," Xi said in a phone call, according to the Xinhua news agency.

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

US Treasury Secretary Scott Bessent, Commerce Secretary Howard Lutnick and Trade Representative Jamieson Greer are leading the US delegation.