China's Commerce Ministry said it "firmly opposes" Trump's move. It gave no indication whether Beijing might make good on threats to retaliate.
Asian stock markets rose Friday on relief that Trump's measures were not more severe. Traders also were encouraged by news 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.
Trump said the tariff hikes ordered Thursday were needed to protect U.S. 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 U.S., who are allies," Taro Kono, Japan's foreign minister, said 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," 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.
Within Asia, demand for steel has grown fastest in developing Southeast Asian economies such as Thailand and Vietnam. The region is dependent on imports to meet its needs, and a large share of Japanese and Chinese steel goes to those markets.
U.S. tariffs could push producers to sell still more to Southeast Asia, depressing steel prices. That would hurt producers but boost profits of construction and other industries in Southeast Asia.
Trump has complained about low-cost Chinese exports of steel and aluminum, but the latest move was likely to hit Japan and South Korea harder.
The United States bought just 1.1 percent of China's steel exports last year compared with 12 percent for South Korea and 5 percent for Japan, according to the U.S. International Trade Commission.
"Significant damage in South Korea's steel exports to the United States seems unavoidable," said Paik's statement.
Australia's trade minister, Steve Ciobo, said he hoped to reach a "positive outcome in the next two weeks" following preliminary discussions with the U.S. trade representative, Robert Lighthizer.
The Chinese Commerce Ministry criticized Trump for taking unilateral action instead of working through the World Trade Organization.
"The misuse of the 'national security exception' clause by the United States is wanton destruction of the multilateral trade system represented by the WTO and will surely have a serious impact on the normal international trade order. China firmly opposes it," said a Commerce Ministry official, Wang Hejun, in a statement.
Beijing said it was ready to retaliate if Chinese companies are hurt, but Friday's statement gave no indication of official action.
"The U.S. 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."
AP writers Mari Yamaguchi and Yuri Kageyama in Tokyo, Youkyung Lee in Seoul and Stephen Wright in Jakarta contributed.
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