While U.S. officials have touted the deal, Chinese officials have been more cautious, emphasizing that the trade dispute has not been completely settled.
Speaking on CBS' Face the Nation, Lighthizer said there would be some routine "scrubs" to the text but "this is totally done, absolutely".
In 2017, before the US-China trade war was unleashed, the United States exported some $120 billion in goods to the Asian giant.
Trump cheered the gains as the Dow Jones Industrial Average picked up another 150 points, tacked onto gains last week after the administration and China announced they were moving forward with a deal to reduce US -imposed tariffs while China commits to new purchases of agricultural products. 'Trade deal set to expand US exports' The "phase one" US-China trade deal reached on Friday is "totally done" despite the need for translation and it will almost double American exports to China over the next two years, US Trade Representative Robert Lighthizer said on Sunday.
The agreement is conducive to gradually bringing China-U.S. economic and trade relations back onto the track of normal development, injecting confidence into the downward world economy and enhancing stability of the global trade order, he said.
In addition, the phase one deal includes structural and other changes to China's economic and trade regime in intellectual property, technology transfer, agriculture, financial services, and currency and foreign exchange. "It takes 90 days and you get real, real enforcement", he said.
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But he would not give a definitive time for top officials to sign the deal, saying of the first week in Januar: 'That's the hope'. The markets continue to receive support from Friday's announcement of an initial trade deal between the United States and China although some analysts are expressing concerns over the lack of details.
"It seems the market has now fully priced the phase 1 trade agreement so we are going to need further news if we are going to push through the important (technical) resistance that is just ahead of crude oil", said Michael McCarthy, chief market strategist at CMC Markets.
In exchange for the Chinese commitments, the Trump administration called off a new round of tariffs that was set to go into effect on Sunday.
A statement issued by the United States Trade Representative on the same day said the U.S. would leave in place 25 per cent tariffs on US$250 billion worth of Chinese goods.
"We know how it's going to end", McConnell said.
"No such offer was ever made to China by the United States".