USA trade representative Robert Lighthizer, who Trump appointed to lead the China talks, is pressing for the U.S. to take a harder line in the negotiations.
They agreed to maintain close contact, the statement said.
"With regard to trade issues and structural problems both sides were concerned about, both carried out extensive, deep, and meticulous exchanges, promoted mutual understanding, and laid the foundation for solving problems that both are interested in", the statement read.
Asked if that meant the talks had been hard, Lu said: "I can only say that extending the consultations shows that the two sides were indeed very serious in conducting the consultations".
Interestingly, while officially this was a vice minister-level dialogue, China's top man for the trade negotiations, Vice Premier Liu He, made an appearance anyway.
The American delegation is led by a deputy US trade representative, Jeffrey D. Gerrish, and includes agriculture, energy, commerce, treasury and State Department officials.
"We urge both governments to use the time remaining in the 90-day negotiating period to make tangible progress on the important issues at the core of the current dispute: equal treatment of foreign companies in China, as well as China's intellectual property and technology transfer policies", said Jake Parker, vice president of China operations at the U.S.
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"Talks with China are going very well!".
The US highlighted China's pledge to purchase more agriculture and other goods, without providing specifics.
Chinese exports to the USA have held up despite tariff increases of up to 25 percent on $250 billion of Chinese imports, partly due to exporters rushing to fill orders before more increases hit.
However, the USTR statement emphasized American insistence on "structural changes" in Chinese technology policy, market access, protection of foreign patents and copyrights and cyber theft of trade secrets.
"It seems there have been no fist fights internally between the two delegations", a person familiar with the progress of the talks told CNN on Tuesday, describing them as "constructive". Trump has been bullish on a possible agreement since before his breakthrough meeting with Chinese President Xi Jinping in Buenos Aires on December 1, and he tweeted on January 8 that "Talks with China are going very well!".
The second day of trade negotiations coincided with an unannounced visit by North Korean leader Kim Jong Un for talks with Xi in Beijing, amid speculation of a second meeting between Kim and Trump.
President Donald Trump campaigned in 2016 on cracking down on what he called Chinese trade abuses, and both countries have been at odds for about a year.
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Should China reform its regulation policies to allow more US access to its markets, USA negotiators want guarantees that they won't erase newfound openness by using government authority to block American companies.
Chinese exports to the United States held up despite the tariff hikes, but that was due partly to exporters rushing to fill orders before any more increases hit.
Beijing on Friday cut bank reserve requirements amid slowing growth at home and pressure from the USA tariffs.
The US trade representative's press office declined to comment.
The Latest on trade tensions between China and the U.S. The escalating trade war raised concerns in China as its economy was on the downward trend amid efforts by the government to rejig the export-dependent economy to that of relying more on domestic consumption.
"China is determined to bring the trade war to an end", The Economist has reported.
China trade talks extended, 'going very well'
The U.S. economy grew at an annual rate of 3.4 per cent in the third quarter and unemployment is at a five-decade low. The trade war has seen both sides impose tariffs on hundreds of billions of dollars worth of goods from each other.