Trump said he has "no deadline" for a deal and didn't mind waiting until after the election next year to make one.
Investors had been hoping for a deal this year, or at least enough progress to stave off new US tariffs on Chinese goods, including smartphones and laptops, scheduled to start December 15.
Wall Street is also weighing the potential for an expanded series of trade disputes after a month of relative calm.
On Tuesday, Trump proposed tariffs on USD 2.4 billion in French products in retaliation for a tax on global tech giants including Google, Amazon and Facebook.
That follows a threat Monday to raise tariffs on steel and aluminum from Argentina and Brazil.
Technology stocks led the losses. The sector is highly sensitive to twists in the trade dispute because many of the companies rely on China for sales and supply chains. Apple slumped 2.5 per cent and Intel fell 2.4 per cent.
Bank stocks also suffered heavy losses as investors headed for the safety of bonds and pushed yields lower.
Banks rely on higher bond yields to charge more lucrative interest rates on mortgages and other loans.
The yield on the 10-year Treasury fell sharply, to 1.74 per cent from 1.83 per cent late Monday.
Bank of America shed 2.3 per cent and Citigroup fell 2.2 per cent.
Utilities and real estate companies held up the best as investors shifted money to the safe-play sectors.