Japan agreed yesterday to give the United States $260 million worth of trade concessions as compensation for continuing to protect its politically powerful leather industry from American competition, administration sources said.

The leather agreement is scheduled to be announced at the White House today by President Reagan, who last September ordered an investigation and possible retaliation against Japan for its barriers to American leather products.

U.S. Trade Representative Clayton Yeutter was reported to have decided to accept Japan's offer of trade concessions rather than retaliate against sales of Japanese products in the United States, despite pressure from Congress and within the administration to punish Tokyo.

The issue is so politically sensitive in Japan that Prime Minister Yasohiro Nakasone wrote a letter to President Reagan on a piece of leather asking that any retaliation be delayed until after Dec. 20, when the Japanese legislature, or Diet, would be out of session. The administration was reportedly ready to announce its retaliatory steps Monday if no agreement was reached over the weekend.

The U.S. had estimated that American leather producers lose $260 million worth of sales because of Japanese protection of its domestic industry, which is run largely by a small sect that controls key districts for Japan's ruling Liberal Democratic Party.

As part of the agreement, Japan will allow imports of U.S. leather products to increase by $24 million, sources said. The rest of the $260 million is the estimated value of the other trade concessions. These other concessions include reducing or eliminating tariffs on 142 items whose sales in Japan totaled $2.9 billion last year. In addition, the Japanese agreed to make permanent a series of temporary cuts in the tariffs on 242 other products. Details of the Japanese concessions are to be announced today.

Japan reportedly gave up some of protection for its aluminum industry, which has come under attack in Congress and been mentioned as a possible target for a Reagan administration investigation.