"I look forward to welcoming China's Vice Premier Liu He to continue these important discussions in Washington next week," he said in the tweet.
Mnuchin and Lighthizer were in the Chinese capital for the first face-to-face meetings between the two sides in weeks after missing an initial end-of-March goal for a summit between U.S. President Donald Trump and Chinese President Xi Jinping to sign a pact.
Trump imposed tariffs on $250 billion of Chinese imports last year in a move to force China to change the way it does business with the rest of the world and to pry open more of China's economy to U.S. companies.
On Thursday, Chinese Premier Li Keqiang said Beijing will sharply expand market access for foreign banks and securities and insurance companies, adding to speculation that China may soon announce new rules to allow foreign financial firms to increase their presence at home.
White House economic adviser Larry Kudlow said the United States may drop some tariffs if a trade deal is reached while keeping others in place to ensure Beijing's compliance.
"We're not going to give up our leverage," he told reporters in Washington on Thursday.
Mnuchin and Lighthizer greeted a waiting Liu at the Diaoyutai State Guest House just before 9 a.m. (0100) on Friday for what China's Commerce Ministry has said would be a full day of talks.
Among Trump's demands are for Beijing to end practices that Washington alleges result in the systematic theft of U.S. intellectual property and the forced transfer of American technology to Chinese companies.
U.S. companies say they are often pressured into handing over technological know-how to Chinese joint venture partners, local officials or regulators as a condition for doing business in China.
The U.S. government says that technology is often subsequently transferred to and used by Chinese competitors.
The issue has proved a tough one for negotiators as U.S. officials say China has previously refused to acknowledge the problem exists to the extent alleged by the United States, making discussing a resolution difficult.
China says it has no technology transfer requirements enshrined in its laws and any such transfers are a result of legitimate transactions.