As the U.S. and Chinese delegations met Wednesday for the start of two days of talks, U.S. Trade Representative Robert Lighthizer welcomed a Chinese team led by Vice Premier Liu He.
"Meetings are going well with good intent and spirit on both sides", he wrote on Twitter Thursday.
The U.S. and China - the world's largest economies - engaged in a bitter tariff fight a year ago over a number of issues including the their bilateral trade imbalance, alleged intellectual property theft by Chinese firms and Beijing's industrial subsidies that put American firms at a disadvantage.
Trump said in his tweets negotiators are working to complete a deal, leaving "NOTHING unresolved on the table" before the March 1 deadline agreed by both sides.
"Hopefully, they're going to buy lots of corn and lots of wheat and lots of everything else that we have, but they're also talking heavy technology, heavy manufacturing services and everything else", Trump said.
If a deal is not reached with Beijing by March 1, the president has said he'll slap another $200 billion in taxes on exports from China.
US and Chinese negotiators are holding high-level talks aimed at settling a six-month trade war that has weakened both sides, shaken financial markets and clouded the outlook for the global economy.
"We hear rumblings or rumors there are some offers (by the Chinese delegation to Washington) around IP (intellectual property) enforcement, around the other sensitive issues". Should the talks fail, U.S. import duties on $200 billion in Chinese imports are due to more than double on March 2.
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But compelling China to reform its trade policies and treatment of foreign companies will be hard.
He pushed Trump to renegotiate NAFTA and vigorously defended the punitive tariffs imposed on U.S. imports of steel and aluminum, a protectionist measure that prompted the departure of Trump's former chief economic adviser, Gary Cohn, who was more pragmatic than dogmatic and highly respected by financial markets.
According to the Wall Street Journal, China trade negotiators proposed a meeting between Xi and Trump in China next month, but the White House has not confirmed a potential summit. The White House did not immediately comment on the report or say when the meeting would take place.
A Chinese delegation is in Washington this week to discuss the broad strokes of an agreement to end the trade war the two countries have fighting for almost a year.
The draft legislation, which was first reviewed by the NPC's Standing Committee in December 2018, is said to ban compulsory technology transfer, guarantee equal treatment of foreign companies, and protect foreign companies' intellectual property rights.
Prior to being named US Trade Representative in May 2017, Lighthizer was a specialist in global trade law for more than 30 years and is a veteran of trade negotiations with Japan in the 1980s.
Moreover, a new complication injected itself into U.S. Treasury Secretary Mnuchin and Commerce Secretary Wilbur Ross have insisted there is no link between the trade talks and Huawei case.
Mr Trump has also threatened tariffs on an additional $267bn worth of products.