The chairmen of 21 House committees and subcommittees with jurisdiction over civil rights matters have written President Reagan, saying his administration's policies "threaten the progress our nation has made in eliminating discrimination."

"The federal government cannot back down from its commitment to civil rights," the letter said, "nor can we relinquish our role as primary guarantors of civil rights."

The letter, dated Wednesday and made public yesterday, was signed by Judiciary Committee Chairman Peter W. Rodino Jr. (D-N.J.), Ways and Means Chairman Dan Rostenkowski (D-Ill.) and 19 other Democratic House leaders.

The letter is the latest round in an increasingly heated struggle over federal civil rights policies and enforcement.

Rep. Patricia Schroeder (D-Colo.) said the battle over Reagan's recent efforts to replace three members of the Civil Rights Commission led to new cooperation among the three minority congressional caucuses--the Hispanic and Black caucuses and the Caucus for Women's Issues--in opposition to what she called "this administration's attack on affirmative action."

"We need to remind the president of the connection between affirmative action policies and the promise of equal employment opportunity in this country," Schroeder said. "By his recent actions, it appears he's forgotten."

On May 25 Reagan submitted to Congress the names of three nominees and fired three of the six members of the independent, bipartisan advisory agency, which was established by Congress to evaluate federal laws and policies on civil rights. The move provoked criticism from civil rights groups and from members of Congress, who expressed concern for the agency's continued freedom from political interference.

Rep. Julian C. Dixon (D-Calif.), chairman of the Congressional Black Caucus, said that Senate confirmation of the three new nominees would mean that Reagan has replaced five of the six commissioners during his administration.

"There is no doubt that such an overhaul will compromise the commission's integrity," he said in a recent letter criticizing the Reagan's action.

In their letter this week, the House leaders asked Reagan to work with the coalition "to ensure that the historical record of bipartisan support for preserving, protecting and defending civil rights in our nation is upheld."

Organizers of the newly formed minority-caucus coalition include Schroeder, who is co-chairman of the Congressional Caucus on Women's Issues, Dixon, chairman of the Black Congressional Caucus, Robert Garcia (D-N.Y.), chairman of the Hispanic Congressional Congress, and Rep. Don Edwards (D-Calif.), chairman of the subcommittee on civil and constitutional rights.