South Korea fell into line yesterday with Reagan administration requests that it trim its steel exports, becoming the last major supplier to go along with the president's program to help American steel makers, administration sources said.

Korean negotiators had stormed out of talks with Deputy U.S. Trade Representative Robert Lighthizer last week, and a ranking Seoul official, Kim Ki-Hwan, accused the Reagan administration of "highly unreasonable treatment to a fair trader."

The Koreans said then they would hold steel sales to the United States at their present level of 2.4 percent of the market, American negotiators demanded 1.7 percent, and they reportedly agreed yesterday on 1.9 percent.

The office of U.S. Trade Representative William E. Brock is expected to announce today the results of its efforts over the past 90 days to reach agreements with major steel suppliers to cut their U.S. exports.

President Reagan announced his program to gain voluntary import restraints Sept. 18 when he rejected a recommendation by the International Trade Commission that he place quotas and tariffs on steel imports. There was no general agreement, though, on whether Brock would be able to reach Reagan's goal of cutting imports to 18 1/2 percent of the American market from their present 26 percent.

Japan, the largest foreign supplier of steel to the United States, was the first nation to agree to cut its exports when it said two weeks ago it would cut exports to 5.8 percent of the U.S. market. Brazil, Spain, South Africa and Australia came in line in the past five days, leaving Argentina as the only holdout among nations being asked to curb shipments.

Korea was angry because U.S. negotiators declined to give Seoul as good a deal as they allowed Tokyo. The European Community already restrains its steel sales and Canada's are expected to remain as is.

In another steel dispute, Reuters reported from Brussels yesterday that Brock offered the 10-nation European Community a 7.6 percent share of the U.S. market for steel pipes and tubes in an effort to head off a possible trade war. Brock last month banned all EC pipe and tube imports for the rest of the year and set a 5.9 percent limit for 1985. EC exports had reached 14.6 percent this year.