Teamsters President William J. McCarthy announced yesterday that he will not seek reelection and a majority of the union's international executive board immediately threw its support behind R.V. Durham, a vice president, to succeed him.

McCarthy, in a brief announcement issued at the conclusion of the board's three-day meeting in West Palm Beach, Fla., cited "personal reasons" for his decision not to run again. McCarthy said he will stay on until December 1991, when national officers will be elected.

The Teamsters are under court order to hold the first direct, secret-ballot elections in the union's history.

A separate announcement, released by a campaign committee being formed to support Durham's candidacy, said "three-quarters of the Teamsters General Executive Board" has announced its support for a slate headed by Durham and Secretary-Treasurer Weldon Mathis, 64. No other candidates for the 21-member slate were announced. Durham, 60, is the head of Local 391 in Greensboro, N.C., and the international union's national freight director.

The announcements ended three days of often bitter confrontation on the board between factions loyal to McCarthy and Mathis and those with allegiance to New York Teamsters leader Joseph Trerotola. Although Trerotola did not receive the backing of the board, he is expected to mount a slate of candidates in next year's elections, probably headed by Walter Shea, another Teamsters vice president.