The offer of the reduction in the surplus was made during the talks in Washington, Reuters said.

One of the sources said that US aircraft maker Boeing would be a major beneficiary of the Chinese offer.

A White House statement released late on Thursday said: “United States officials conveyed the President’s clear goal for a fair trading relationship with China. United States officials and the Chinese delegation also participated in a meeting with President Donald J Trump at the White House. The two sides agreed to continue the discussions on Friday.”

Liu told Trump the two countries needed to properly resolve their trade disputes in an equal and mutually beneficial way, the Chinese state-run news agency Xinhua reported.

“China is willing to work with the US to properly resolve economic and trade issues that concern both nations in an equal and mutually beneficial manner,” Liu was quoted as saying. “Both sides should ensure economic and trade cooperation continue to be the driver of Sino-US relations.”

Trump was quoted by Xinhua as saying the two countries should expand cooperation in energy, manufacturing, investment and agricultural imports, while improving market access.

The US president also said he has built a good personal and working relationship with Chinese President Xi Jinping.

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Trump, however, was more critical of China in comments made during an earlier meeting on Thursday with Nato Secretary General Jens Stoltenberg.

Trump said the US has been “ripped off by China” for years and denied that his comments about helping resolve US sanctions on the Chinese telecommunications giant ZTE meant his administration was going soft on Beijing.

The president also suggested Xi may have influenced North Korea’s leader, Kim Jong-un, to take a harder line against the US ahead of a planned Trump-Kim summit.

“We lost US$800 billion on trade last year, of which China was US$500 billion,” Trump said ahead of the meeting with Liu.

Concerning ZTE, the US Department of Commerce initiated a ban last month on sales of components by American companies to the Chinese telecommunications equipment maker. The department said that ZTE had been making false statements about measures it had agreed to take against employees running a unit that was doing business with Iran in violation of sanctions.

Trump, however, pledged on Twitter on Sunday to help give ZTE “a way back into business, fast”, after the company was banned from buying components from US suppliers for seven years. “Too many jobs in China lost. Commerce Department has been instructed to get it done!” Trump tweeted.

That drew accusations that his treatment of the company contradicted his hardline approach to national security threats, particularly with respect to Beijing.

On Thursday, Trump defended himself, saying that the commerce department sanctions had his approval and that no decision had yet been made to retract them.

Regarding North Korea, and its abrupt announcement Wednesday that it might back out of the Trump-Kim summit meeting planned for June 12 in Singapore, Trump said that Xi “could be influencing” Kim.

“If you remember two weeks ago, all of a sudden out of nowhere Kim Jong-un went to China to say hello again – second time – to President Xi,” Trump told reporters, referring to a May 8 meeting between the leaders.

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“It could very well be that he’s influencing Kim Jong-un. We’ll see what happens,” Trump said.

White House press secretary Sarah Huckabee Sanders said that the administration was continuing to prepare for Singapore. Trump also said that if the meeting did not take place, the administration would move on.

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“If the meeting happens, it happens, and if it doesn't we go on to the next step,” Trump said. “Our people are literally dealing with them right now in terms of making arrangements.”

The meeting between Trump and Liu was not on the White House schedule or mentioned in the US State Department’s recent announcement about the trade talks.

“The president is meeting with Liu this afternoon,” National Economic Council director Larry Kudlow told White House reporters in the morning. “It means that there’s great interest here in furthering the deal and furthering negotiations and trying to reach some remedies regarding unfair and illegal trading practices.”

Treasury Secretary Steven Mnuchin is leading the trade negotiations, along with Commerce Secretary Wilbur Ross and US Trade Representative Robert Lighthizer, whose department is currently holding hearings in Washington with US companies and industry associations about proposed punitive tariffs on imports from China.

Liu‘s trip to America is his second in three months and follows the recent visit to Beijing by the US delegation led by Mnuchin, which ended without tangible achievements.

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Liu’s visit is the latest stage in near continuous negotiations aimed at preventing a tariff war from breaking out. The trade representative’s office (USTR) could start levying US$50 billion in import taxes on Chinese goods any time after hearings and public feedback end on Tuesday.

China retaliated against USTR’s plan by announcing tariffs on an equivalent amount of US imports. Trump then threatened to target another US$100 billion worth of Chinese goods.

When Mnuchin’s team held talks with Liu earlier this month, the only result was an agreement to continue negotiating. Chinese President Xi Jinping did not meet anyone from the US delegation during that trip.

Mid-level officials from China’s commerce ministry met with their counterparts in Washington last week to prepare for Liu’s arrival, reportedly looking for ways to trim the US trade deficit with China by US$200 billion.

That deficit hit a record US$375 billion in 2017 and has continued rising this year.

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Xinhua reported earlier on Thursday that Liu met US elder statesman Henry Kissinger and lawmakers including Orrin Hatch, the Utah Republican who is chairman of the Senate Finance Committee, shortly after arriving in Washington.

Lie “will actively explore a proper settlement of the trade issues so as to secure a healthy development of the economic and trade ties between Beijing and Washington”, Xinhua said.

Hatch issued a statement saying that he emphasised to Liu “the importance of respecting intellectual property rights and the ability of American businesses to export and do business in China without being forced to transfer technology to Chinese companies – goals I share with the Trump administration.”

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Regulations in China that force foreign companies operating there to transfer intellectual property and proprietary technology to joint venture partners, as well as Beijing’s state-directed financial support for domestic technology companies, prompted Trump to order USTR to draw up its tariff plan against China.

“While imposing tariffs would harm both countries, the theft of American intellectual property in China is a persistent and serious problem that must stop,” Hatch said.