Market benchmarks in Shanghai, Tokyo, Hong Kong and Southeast Asia all declined.
Trump said Tuesday agreement on the "Phase 1" deal announced last month "could happen soon." But he warned he was ready to raise tariffs "very substantially" if that fails.
The two sides disagree publicly about whether Washington agreed to roll back some punitive tariffs imposed in the fight over Beijing's trade surplus and technology ambitions. The Chinese government said last week that was settled, but Trump denied that.
Trump's comments "served as a reminder of the challenge that the two sides face," said Jingyi Pan of IG in a report. However, she said, investors saw them as "positioning statements," reducing their impact.
Trump's comments did little to jolt Wall Street, which closed with modest gains.
The Shanghai Composite Index lost 0.4% to 2,905.06 and Tokyo's Nikkei 225 sank 0.9% to 23,3154.90. Hong Kong's Hang Seng tumbled 2% to 26,511.11.
South Korea's Kospi retreated 0.9% to 2,123.74 and Australia's S&P-ASX 200 sank 0.8% lower at 6,698.30. India's Sensex opened down 25 points at 40,319.59. Taiwan, New Zealand and Singapore also declined.
Hong Kong shares have been jolted by growing violence in the anti-government protests. Police shot a protester in a scuffle Monday and a man who was defending China in an apparent argument was set on fire. Activists also this week have damaged trains and transit stations while clashing with police using tear gas and other crowd control measures.
The protests began in June over an extradition bill that was subsequently withdrawn, but the movement expanded to demands for greater democracy, police accountability and other grievances. The protests, the U.S.-China tariff war and economic factors have sent Hong Kong tumbling into its first recession in a decade.
On Wall Street, the benchmark S&P 500 index rose past the 3,100 level for the first time, but the gains didn't hold. The index ended up 0.2% at 3,091.84.
The Dow Jones Industrial Average closed unchanged at 27,691.49. The Nasdaq gained 0.3% to a record 8,486.09.
Momentum for the market has been mostly upward for more than five weeks as worries about the U.S.-China trade war have eased, among other factors.
Health care, technology and communication services stocks led gains Tuesday, outweighing losses in energy companies and elsewhere.
This week, the U.S. Labor Department is due to give updates on consumer and wholesale inflation. Economists expect a government report to show retail sales returned to growth in October.
Federal Reserve Chairman Jerome Powell is due to give testimony to Congress on Wednesday about the U.S. economy. Most investors expect the Fed to keep interest rates on hold for now after cutting them three times since the summer.