Antal Dorati has resigned his title as music director of the Detroit Symphony Orchestra as the result of differences with the new salaried president of the orchestra, Louis A. MacKenzie. But if those differences are rectified, he has offered to resume the title and to make a $50,000 contribution to the orchestra.

In a six-page letter sent to Robert Semple, chairman of the orchestra's board of directors, and to the Detroit Free Press, Dorati outlined his concerns for the future of the ensemble. The Free Press published the letter in full yesterday.

Dorati is concerned about the recent cancellation of some radio broadcasts, the lack of support for a civic orchestra which he hoped would become a training orchestra for the Detroit Symphony, and other budget cuts.

His resignation, however, applies only to his role as music director. Stating that he would be present to fulfill his contractual obligations for the opening of the season on Sept. 21, Dorati said that he would serve without the title, continuing to conduct and giving attention to the areas of future planning and auditions. He went on to say that "if corrective measures were taken," he and his wife, pianist Ilse von Alpenheim, would contribute $50,000 to the orchestra's fund at the time of his 75th birthday next April 9.

Noting that that sum was not an insignificant amount in his financial situation, Dorati pointed out that there were a number of people living in the Detroit area who, if they were to contribute a proportionate amount of their resources, would give the orchestra $5 million.

Semple said yesterday that he would be in touch with Dorati, who is in Paris, and that he hoped matters could be worked out to their mutual satisfaction. Dorati's present contract with the Detroit Symphony extends through the spring of 1982.