The Shanghai Composite index plunged 5.2% to 2,918.65, and the Hang Seng in Hong Kong sank 3.4% to 29,060.87. The future contract for the Dow Jones Industrial Average fell 1.9% to 26,003.00, while that for the S&P 500 also shed 1.9%, to 2,892.20.
His comments Sunday came as a Chinese delegation was due to resume talks in Washington on Wednesday aimed at resolving a tariffs battle that has rattled world markets.
The Wall Street Journal, citing unidentified sources, said China's government was considering canceling this week's talks. Chinese officials have emphasized they would not negotiate under pressure.
Without fresh reassurances, markets were swooning.
Japan's markets were closed for a holiday, but the future contract for the benchmark Nikkei 225 index lost 2.5%.
Shares also fell sharply in Taiwan, Singapore, Australia and Indonesia.
Apparently catching Beijing by surprise, Trump said he would raise import taxes on $200 billion in Chinese products to 25% from 10% as of Friday.
Trump said "The Trade Deal with China continues, but too slowly, as they attempt to renegotiate. No!"
The comments came as a surprise to many who had been anticipating a possible deal as early as this week in the dispute over Chinese industrial policies and technology.
"Arguably, Trump's threat to lift tariffs 'shortly' if Beijing does not play ball on US trade demands, may be more a negotiations tactics than an imminent trade action," Mizuho Bank said in a commentary.
"Nonetheless, Trump's tweet allusions to tariffs being 'partially responsible for ... great (US) economic results' does raise the threat of misguided trade policy" from the U.S, it said.
The revived tensions over trade caused oil prices to sink. Benchmark U.S. crude shed $1.49, or 2.4%, to $60.46 per barrel in electronic trading on the New York Mercantile Exchange. It gained 13 cents to $61.94 per barrel on Friday.
Brent crude, the international standard, gave up $1.57, or 2.2%, to $69.28 per barrel. It rose 10 cents on Friday to $70.85 per barrel.
The turmoil in other markets pushed the Japanese yen, viewed as a safe haven for investors, higher against the dollar. The greenback was trading at 110.60 Japanese yen by midday Monday, down from 111.11 yen on Friday.
The euro weakened to $1.1195 from $1.1200 on Friday.