The United States and South Korea agreed to revise a trade pact sharply criticized by U.S. President Donald Trump, Seoul said on Monday, with U.S. automakers winning improved market access and Korean steelmakers hit with quotas but avoiding hefty tariffs.

The planned changes in the U.S.-Korea Free Trade Agreement (KORUS) were seen as limited, leaving South Korea's key passenger car exports untouched and helping soothe fears that Trump's tough approach could start a spiraling global trade war.

In April, Trump told Reuters he would either renegotiate or terminate what he called a "horrible" trade deal that has doubled the U.S. goods trade deficit with South Korea since 2012.

Asian shares steadied on Monday, stemming last week's hefty losses after Trump's action on steel and aluminum, and his plans to slap tariffs on up to $60 billion in Chinese goods.

The agreement means South Korea will be forced to cut its steel exports to the U.S. by 30 percent of past three years' average, in exchange for becoming the first U.S. ally to receive an indefinite exemption on steel tariffs imposed by Trump.

"We had heated discussions," South Korean Trade Minister Kim Hyun-chong said at a media briefing in Seoul. "The latest agreement removed two uncertainties," he said, referring to steel tariff exemptions and KORUS renegotiation.

Last week, Trump temporarily excluded six trade partners, including Canada, Mexico and the European Union from higher U.S. import duties on steel and aluminum which came into effect on Friday.

South Korea has received a quota of about 2.68 million tonnes of steel exports, or 70 percent of the annual average Korean steel exports to the United States between 2015-2017, which will be exempt from the new tariffs, the ministry said in a statement.

South Korea is not allowed to export steel products exceeding that quota to the U.S. market, a ministry official said.

"This leaves a bad precedent of exchanging steel tariffs - which is a breach of international trade law - for a legitimate free trade agreement, in negotiations," said Wonmog Choi, professor of law at Ewha Womans University.