Economists say quick breakthroughs are unlikely because the two governments face the same disagreements over China's technology policy and trade surplus that caused talks to break down in May. Trump and President Xi Jinping agreed in June to resume negotiations but neither side has given any sign it might offer big concessions.
The dispute over U.S. complaints that Beijing steals or pressures companies to hand over technology has battered exporters on both sides and disrupted trade in goods from soybeans to medical equipment.
U.S. Trade Representative Robert Lighthizer, Treasury Secretary Steven Mnuchin and their Chinese counterpart, Vice Premier Liu He, smiled and shook hands but said nothing to reporters as they began a meeting at a government guesthouse in Shanghai. That followed an official dinner Tuesday at the elegant Peace Hotel on the waterfront Bund.
Trump has raised tariffs on $250 billion worth of Chinese imports. Beijing responded by taxing $110 billion of U.S. products.
Chinese leaders are resisting U.S. pressure to roll back plans for government-led development of industry leaders in robotics, artificial intelligence and other technologies. Washington complains those efforts depend on stealing or pressuring foreign companies to hand over technology.
For their part, American negotiators have resisted Chinese demands that punitive U.S. tariffs be lifted immediately. Trump wants to keep some penalties in place to ensure Beijing carries out any agreement.
Rhetoric on both sides has hardened, prompting some economists to suggest U.S. and Chinese leaders are settling in for a "war of attrition."
In Washington, Trump accused Beijing of wanting to stall through the 2020 presidential election in hopes of being able to negotiate with a more malleable Democrat. He said that if re-elected, he would get "much tougher" with Beijing.
"China would love to wait and just hope," Trump told reporters Tuesday.
"They'll pray that Trump loses," he said. "And then they'll make a deal with a stiff, somebody that doesn't know what they're doing."
Separately on Twitter, Trump warned that if he wins in 2020, "the deal that they get will be much tougher than what we are negotiating now ... or no deal at all."
Negotiators in Shanghai are also expected to discuss the fate of telecom equipment giant Huawei Technologies Ltd. Washington put the company, China's first global tech brand, on a security list in May that blocks purchases of U.S. components and technology.
The United States say Huawei is a national security threat, an accusation the company denies. Trump has said it could be a bargaining chip in the trade dispute.