As Trump presses ahead with plans to reorder the global economy with the highest tariff rates since the early 1930s, Switzerland, "stunned" by 39 per cent tariffs, sought more talks, as did India, hit with a 25 per cent rate.
New tariffs announced on Friday also included a 35 per cent duty on many goods from Canada, 50 per cent for Brazil, 20 per cent for Taiwan, which said its rate was "temporary" and it expected to reach a lower figure.
The presidential order listed higher import duty rates of 10 per cent to 41 per cent starting in a week's time for 69 trading partners, taking the US effective tariff rate to about 18 per cent, from 2.3 per cent last year, according to analysts at Capital Economics.
US stocks took a hit. By afternoon on Friday, the Dow Jones Industrial Average had dropped 1.46 per cent to 43,486.45, the S&P 500 1.8 per cent to 6,225.55 and the Nasdaq Composite 2.42 per cent to 20,610.91.
Markets were also reacting to a disappointing jobs report. Data showed US job growth slowed more than expected in July while the prior month's data was revised sharply lower, pointing to a slowdown in the labour market.
Global shares stumbled, with Europe's STOXX 600 tumbling 1.89 per cent on the day.
Trump's new tariffs have created yet more uncertainty, with many details unclear. They are set to take effect on August 7, a White House official said.
Trump administration officials defended the president's approach saying the uncertainty was "critical" for him to be able to leverage a better deal.
"The trade deals we've seen over the last few weeks... have been nothing short of monumental," Council of Economic Advisers Chair Stephen Miran said on CNBC.
Trump's tariff rollout also comes amid evidence they have begun driving up prices of home furnishings and household equipment.
Australian products could become more competitive in the US market, helping businesses boost exports, Trade Minister Don Farrell said, after Trump kept the minimum tariff rate of 10 per cent for Australia.
The European Union, which struck a framework deal with Trump on Sunday, is still awaiting more Trump orders to deliver on agreed carve-outs, including on cars and aircraft, EU officials said, saying the latest executive orders did not cover that.
Switzerland said it would push for a "negotiated solution" with the US, with industry insiders saying they were "stunned" by the 39 per cent tariffs.
South Africa's Trade Minister Parks Tau said he was seeking "real, practical interventions" to defend jobs and the economy against the 30 per cent US tariff it faces.
Southeast Asian countries largely breathed a sigh of relief after the US tariffs on their exports that were lower than threatened and leveled the playing field with a rate of about 19 per cent across the region's biggest economies.
Thailand's finance minister said a reduction from 36 per cent to 19 per cent would help his country's economy.
While India is in talks after being slapped with a 25 per cent tariff, which could impact about $US40 billion ($A62 billion) worth of its exports.
Trump issued a separate order for Canada that raises the rate on Canadian goods subject to fentanyl-related tariffs to 35 per cent, from 25 per cent previously, saying Canada had "failed to cooperate" in curbing illicit narcotics flows into the US.
This is contrast to his decision to allow Mexico a 90-day reprieve from higher tariffs to allow time to negotiate.
Businesses and analysts said the impact of Trump's new trade regime would not be positive for economic growth.
"No real winners in trade conflicts," said Thomas Rupf, co-head Singapore and CIO Asia at VP Bank.
"Despite some countries securing better terms, the overall impact is negative."
