China has accused Donald Trump of damaging the global trading system by hiking steel and aluminium tariffs, while Japan and South Korea expressed alarm at potential economic damage.
China's Commerce Ministry said it "firmly opposes" the US president's move, but gave no indication whether Beijing might make good on threats to retaliate.
Asian stock markets rose in early trading on relief that Mr Trump's measures were not more severe.
Traders also were encouraged by news Mr Trump might meet North Korean leader Kim Jong-un.
South Korea's trade minister, speaking at an emergency meeting, appealed to other governments to prevent a "trade war".
"We will urge the international community to refrain from adopting measures that inhibit free trade," said the minister, Paik Un-gyu, according to a ministry statement.
Mr Trump said the tariff hikes ordered yesterday were needed to protect US national security by ensuring the survival of the country's metals producers.
"These measures could make a significant impact on the economic and cooperative relationship between Japan and the US, who are allies," said Taro Kono, Japan's trade minister, in a statement.
The new tariffs take effect in 15 days, with Canada and Mexico indefinitely spared "to see if we can make the deal," Mr Trump said, referring to a possible renegotiation of the North American Free Trade Agreement.
He suggested at a Cabinet meeting that Australia and "other countries" might be spared, a shift that could soften the blow amid threats of retaliation.
Mr Trump has complained about low-cost Chinese exports of steel and aluminium, but the latest move was likely to hit Japan and South Korea harder.
The United States bought just 1.1% of China's steel exports last year compared with 12% for South Korea and 5% for Japan, according to the US International Trade Commission.
"Significant damage in South Korea's steel exports to the United States seems unavoidable," said Mr Paik's statement.
Australia's trade minister said he had preliminary discussions with the US trade representative, Robert Lighthizer.
The minister, Steve Ciobo, expressed hope of "finalising a positive outcome in the next two weeks".
The Chinese Commerce Ministry criticised Mr Trump for taking unilateral action instead of working through the World Trade Organisation.
Beijing said it was ready to retaliate in the event Chinese companies are hurt, but Friday's statement gave no indication of official action.
"The US pursues trade protectionism," said the China Iron & Steel Association, an industry group, in a statement.
"This move will harm the global steel industry, and seriously hurt consumers' interests," said the statement. It said the United States "will injure others and harm itself."