While Liu said the negotiations have made "great progress", US Trade Representative Robert Lighthizer noted there were "some major issues" still left to resolve.
The issue is one of a host of USA complaints that the administration of President Donald Trump is demanding China address if it wants to end trade disputes that have cost both countries billions of dollars and slowed the global economy.
"This is the granddaddy of them all". However, an article from the Chinese news agency Xinhua on Thursday said Xi had delivered a message to Trump that substantial new progress has been made and that he encouraged the two sides to conclude the deal as soon as possible.
Earlier in the day Mr Trump told reporters that discussions are going "very well" but downplayed any further speculation. "We are rounding the turn".
This is despite the high buzz that the two sides have ironed out most differences and are heading towards a deal.
Mr. Trump's upbeat remarks came on the second of three days of talks this week between USA and Chinese negotiators.
"If it's not a great deal, we're not doing it". Three days later, he predicted that he would sign a deal "fairly soon".
Meanwhile, a bipartisan group of Senators introduced the Fentanyl Sanctions Act - the first-ever fentanyl sanctions bill - that would apply pressure on the Chinese government to honour their commitment to make all fentanyl illegal and provide the United States with more tools and resources to go after illicit traffickers in China, Mexico and other countries. Mr Lighthizer, Mr Mnuchin and Mr Liu held a working dinner Tuesday night, according to one of the people.
Vice Premier and Beijing's trade envoy Liu flew to Washington this week to continue hammering out trade negotiations.
Various reports citing people familiar with the negotiations indicate the potential agreement would give China until 2025 to deliver on its pledges to buy more goods from the US. The current round of talks is scheduled to go through Friday and possibly longer. We have to make sure there's enforcement.
He also described it as potentially "epic" and "historic".
Washington wants sweeping changes to China's economic and trade policies, while Beijing wants Trump to lift expensive sanctions on Chinese goods. In retaliation, China has targeted $110 billion in American imports. Trump's tariffs won't solve this trade imbalance problem. Those would be binding pledges that could trigger U.S. retaliation if unfulfilled, according to the people, who asked not to be identified because the talks are private. China in turn is fighting back against agreeing to more hard structural changes Washington that is demanding.
The president also said he still wants to meet Chinese President Xi Jinping.
China has unquestionably fared much worse than the United States during the Trump trade war, defying the predictions of most analysts. "But we're not there and we hope this week to get closer", he said. During his presidential campaign, he assailed China for the "rape" of the American economy. -China trade and it will be "closer to being a cease-fire".
Separately, Chinese commerce ministry spokesperson Gao Feng announced reciprocal suspension of additional tariffs slapped by both the countries on each other's goods since previous year, saying the move would "undoubtedly" create a conducive atmosphere for the China-US economic and trade negotiations. Trump has bragged of a friendly relationship with the Chinese leader.
Mr Trump has also threatened further tariffs on an additional $267bn worth of Chinese products - which would see virtually all of Chinese imports into the United States become subject to these tariffs.
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