Senate Majority Leader Robert J. Dole (R-Kan.) said yesterday that the Reagan administration has abandoned efforts to salvage the nomination of William Bradford Reynolds to be associate attorney general.

Dole said the decision to cease efforts on behalf of President Reagan's leading spokesman on civil rights was reached after discussions with White House chief of staff Donald T. Regan and Attorney General Edwin Meese III.

Reynolds' nomination was rejected by the Senate Judiciary Committee last month. But administration officials recently enlisted Dole's help in trying to force a vote on the nomination by the full Senate. They also considered giving Reynolds a recess appointment after Congress adjourns in August.

But Senate reaction to the idea was sharply negative, and a Republican source said Dole told the White House there were only 40 GOP votes for pushing the nomination, far short of the majority vote needed to take it to the floor.

Two Judiciary Committee Republicans -- Arlen Specter (Pa.) and Charles McC. Mathias Jr. (Md.) -- had joined all eight Democrats in arguing that Reynolds has been lax in enforcing civil rights laws and that he repeatedly misled the panel in sworn testimony. Reynolds has said he would stay on as head of the department's Civil Rights Division if he was denied promotion.

Dole's announcement came as another congressional panel prepared to criticize the administration's civil rights record at a hearing today. A House Government Operations subcommittee, headed by Rep. Ted Weiss (D-N.Y.), plans to ask why little progress has been made in civil rights cases initiated by the Education Department.

Figures compiled by civil rights attorneys show that Reynolds has taken no action in 19 of 23 discrimination cases referred to his office by the Education Department in the last four years. Most of the cases involve sex discrimination, education for handicapped students and racially segregated classes.

Reynolds has not acted on 15 of the cases and has sent four back to the Education Department; most of these cases were referred to him at least two years ago. Reynolds has filed suit in three school desegregation cases. One was resolved through a voluntary agreement.

"The dirty little secret about this is the Justice Department has usually not done anything with the cases referred," said Phyllis McClure, an attorney with the NAACP Legal Defense and Education Fund, which obtained the data.

John V. Wilson Jr., a spokesman for Reynolds, said the department's record was "not a matter of no action. All of them are under investigation."

The Justice Department must "evaluate each referral on its merits and its suitability for litigation," Wilson said. Some cases were sent back because "we needed additional information," he said, and the other cases are being actively investigated or are the subject of negotiations in an effort to reach agreement before going to court.

Thomasina Rogers, a spokesman for the Education Department's Office of Civil Rights, said her office must "evaluate whether some other course of action is available to us" in cases that Justice has declined to pursue.

When it finds evidence of discrimination and cannot settle a case through voluntary means, the Education Department must send the case to Justice or begin an administrative proceeding. The latter course can lead to a cutoff of federal funds for the affected institution.

Rogers said some cases are referred to Justice because administrative hearings can be "unwieldy and impractical" and cutting off funds may be too severe a remedy.

Reynolds has said that criticism of his civil rights record in such areas as housing and employment is based on his opposition to sweeping, race-conscious remedies such as busing and quotas. But most of the education cases, which have received less public attention, do not appear to involve such philosophical disputes.

Many of the referrals to Justice came just before a court-imposed deadline of Sept. 7, 1983. U.S. District Court Judge John Pratt, ruling in a 1970 lawsuit, ordered the Education Department to dispose of its case backlog by that date.

Harry M. Singleton, chief of Education's civil rights office, said in a recent deposition that "once a case is referred to Justice for action, that's their responsiblity."

David Tatel, who held Singleton's job during the Carter administration, said only cases involving novel legal issues should be sent to Justice. He said referring a case to Justice "is one way to get it off their plate and onto someone else's. It's a way of dumping cases."

In a case involving Dillon County, S.C., Singleton told Reynolds in a 1983 letter that the school district had created racially segregated classes by grouping students according to ability. Singleton said the district could provide "no adequate justification" for the groupings.

Wilson said Justice needed more information on the case. Rogers said the Education Department is studying it further.

McClure of the NAACP Legal Defense and Education Fund criticized Reynolds for failing to file suit in three cases in which Education officials found evidence of sex discrimination against individual school employes. In a case in Anna, Ill., Reynolds said a woman who was demoted "is the only person who may have been subject to the [sex discrimination] violation . . . . There is no evidence to suggest that [the district] is engaged in a pattern of discrimination."

"Reynolds is the one who has strenuously argued that the civil rights laws guarantee rights to individuals, not groups," McClure said. "Then he turns around and says there's only one individual in these cases and there's no pattern and practice. You're caught in this Catch-22."

But Wilson said the Justice Department decided that the sex bias cases were "unattractive" because the plaintiffs had filed private lawsuits and lost for procedural and other reasons. "That's a prosecutorial judgment," he said.