In early trading, Tokyo's main index tumbled 2.2% and Hong Kong's benchmark lost 2%. Markets in Shanghai, Sydney and Seoul also fell.
Trump's announcement of 10% tariffs on $300 billion of Chinese goods, due to take effect Sept. 1, surprised investors after the White House said Beijing promised to buy more farm goods. That came as their latest round of trade talks ended in Shanghai.
That added to investor unease following Federal Reserve Chairman Jerome Powell's suggestion Wednesday that the U.S. central bank had no plans for an extended cycle of interest rate cuts.
"Markets are reeling after President Trump expressed his frustration with China's stalling techniques," said Stephen Innes of VM Markets in a report. "With the global markets on edge after Chair Powell's communication failed so miserably, few traders have been willing to step in front of this steamroller."
The Shanghai Composite Index lost 1.4% to 2,867.20 while Tokyo's Nikkei 225 declined to 21,047.38.
Hong Kong's Hang Seng fell to 26,998.20. Seoul's Kospi shed 1% to 1,998.06 and Sydney's S&P-ASX 200 retreated 0.7% to 6,762.30. Markets in New Zealand, Taiwan and Southeast Asia also fell.
On Wall Street, the benchmark Standard & Poor's 500 fell for a fourth day, losing 0.9% to 2,953.56.
The Dow Jones Industrial Average declined 1% to 26,583.42. The Nasdaq composite ended 0.8% lower at 8,111.12.
The escalation in U.S.-Chinese trade tension comes only a couple of days after both sides resumed negotiations.
In a series of tweets, Trump noted that while slow-moving negotiations have been "constructive," China has not followed through on some prior agreements.
Washington has imposed tariffs of 25% on $250 billion worth of Chinese goods over complaints Beijing steals or pressures companies to hand over technology. Beijing retaliated with tariffs on $110 billion of American goods, including agricultural products, in a direct shot at Trump supporters in the U.S. farm belt.
Unlike earlier tariffs, which were meant to minimize the impact on ordinary Americans by targeting industrial goods, the new ones would affect a wide range of consumer products.
Trump also expressed frustration the Fed isn't cutting interest rates more aggressively.
The Fed cut its key interest rate for the first time in a decade Wednesday, citing uncertainty over the U.S. trade conflicts.
U.S. share price declines come despite unexpectedly strong corporate earnings.
Oil companies Exxon and Chevron will report results on Friday. The government will also release its employment report for July on Friday.
Qualcomm fell 2.7% after the chipmaker gave investors a surprisingly weak profit and revenue forecast because of problems in China. A ban on exports to China's Huawei, which is part of the ongoing trade war between the U.S. and China, hangs over the company.
ENERGY: Benchmark U.S. crude jumped 99 cents to $54.94 per barrel in electronic trading on the New York Mercantile Exchange. The contract plunged $4.53 on Thursday — its biggest drop in more than four years — to $53.95. Brent crude, used to price international oils, soared $1.51 to $62.01 per barrel in London. It fell $4.55 the previous session to $60.50.
CURRENCY: The dollar declined to 107.04 yen from Thursday's 107.35 yen. The euro edged down to $1.1076 from $1.1085.