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 says it "firmly opposes" the US president's move but gave no indication whether Beijing might make good on threats to retaliate.
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," Paik Un-gyu told a meeting of steelmakers, according to a ministry statement.
Trump said the tariff hikes ordered on Thursday 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 co-operative relationship between Japan and the US, who are allies," Japanese Trade Minister Taro Kono said in a statement.
The European Union, Brazil and Argentina said overnight they should not be targeted or would seek exemptions, and Japan and South Korea also said they would seek exceptions.
Trade tensions between China and US have risen since Trump took office. China accounts for only a small fraction of US steel imports but its industrial expansion has helped create a global steel glut that has driven down prices.
The Chinese commerce ministry criticised Trump for taking unilateral action instead of working through the World Trade Organisation.
"The misuse of the 'national security exception' clause by the United States is wanton destruction of the multilateral trade system represented by the WTO (World Trade Organisation) and will surely have a serious impact on the normal international trade order. China firmly opposes it," ministry official Wang Hejun said on Friday.
Beijing said it was ready to retaliate in the event Chinese companies were hurt.
Trump's declaration coincided with the signing by 11 countries of a new Trans-Pacific trade pact the US withdrew from last year.
Australian Prime Minister Malcolm Turnbull sounded confident of getting favourable treatment as Trump spoke of Washington's strong relationship with Australia, a major exporter of iron ore but exports little steel.
"There is no case for imposing tariffs on Australian steel," Turnbull said.