Thirty-seven civil rights and labor groups, led by the AFL-CIO, have sent a letter to President Reagan's budget director, David A. Stockman, expressing their opposition to proposed changes in a key federal affirmative action program.

"We are united in our opposition ot changes which would sound the death knell for the federal contract compliance program, for 40 years a vital element in the national effort to provide equal employment opportunity," said the letter, signed by AFL-CIO President Lane Kirkland.

Among the groups endorsing the protest letter were the League of Women Voters, the NAACP, the National Bar Association, the National Organization for Women, the National Urban League, the United Mine Workers, the United Auto Workers, the East Tennessee Coalmining Women's Support Team and the Mexican American Legal Defense and Educational Fund.

The proposals, which rely "largely on self-monitoring by contractors," will be seen by those employers as "a signal for backsliding," the letter said.

Officials of the Labor Department, which includes the compliance office, have announced tentative changes in regulations which would, among other things, reduce the number of companies covered by affirmative action requirements, reduce reporting requirements and generally trim the government's control over employers who do business with the government.

President Reagan has given Stockman and the budget office final authority over any such regulatory changes.