Days before chief justice-designate William H. Rehnquist's confirmation hearings, another Phoenix lawyer has contradicted Rehnquist's 1971 testimony about his role in a 1960s Republican election program to reduce voting in the city's heavily Democratic minority precincts.

The issue is expected to be one of the major ones raised against the 61-year-old Supreme Court associate justice, nominated by President Reagan to succeed Warren E. Burger, who is retiring. However, the dispute, although it will be discussed at the hearings that begin Tuesday, is not expected to slow the nomination, much less block it.

The lawyer, Melvin Mirkin, who knew Rehnquist as a fellow Stanford Law School alumnus, said Rehnquist was part of a group of Republican activists who turned up at a largely black and Hispanic precinct early one election day and announced that they were there to challenge credentials of the voters waiting in line.

Mirkin's recollections, along with those of a number of other Phoenix Democrats, contradict Rehnquist's 1971 account of his role as a Republican Party leader in charge of "ballot security" and similar programs between 1958 and 1964.

Rehnquist declared that "in none of those years did I personally engage in challenging the qualifications of any voters."

Two Democratic members of the Senate Judiciary Committee, Howard M. Metzenbaum of Ohio and Paul Simon of Illinois, have asked for an expedited FBI inquiry into the dispute. It is one of the issues expected to be aired when Rehnquist goes before the committee for his confirmation hearings. He is expected to be the first of more than 30 witnesses.

Committee Chairman Strom Thurmond (R-S.C.) said in a brief news conference Friday that he thinks that Rehnquist will be confirmed as chief justice "without any trouble" and that the new allegations are "not sufficient to tarnish him."

"Any matters that were known prior to his confirmation" in 1971 as associate justice on the court, Thurmond said, "seem settled."

However, Joseph L. Rauh Jr., a founder of the Leadership Conference on Civil Rights, which opposes Rehnquist, said, "There is a prayer" that Rehnquist will not be confirmed.

"Even if you lose," Rauh said, "it would be obscene to let this guy through without a fight. You have to make a fight."

Democratic senators unhappy with the nomination, sources said, will question Rehnquist on the views he expressed on racial matters as a Supreme Court clerk in 1952-53 and on his refusal to disqualify himself in a controversial 1972 Army surveillance case.

Rehnquist's conservatism is likely to be challenged by critics who consider him too much of an extremist to be chief justice.

Rehnquist has been alone in dissent more often than any other justice on the Burger court, although that court has been viewed generally as a moderate-to-conservative institution.

His dissents often stem from his view that the Constitution as first drafted was not enacted to guarantee individual freedom but rather to curtail it, and that the Constitution, even as amended after the Civil War, does not grant the federal government or the federal judiciary much power to protect fundamental individual rights from state regulation.

There may also be an effort, sources said, to use the Phoenix voter-harassment allegations as part of a broad attack on Rehnquist's credibility.

Some committee Democrats may try to show that Rehnquist was not candid with the committee in 1971 when questioned about a memorandum he wrote as a Supreme Court clerk to Justice Robert H. Jackson, involving the 1954 Brown v. Board of Education school desegregation case.

In the memo, Rehnquist supported the "separate-but-equal" doctrine of racial segregation. In a letter to the 1971 committee, however, Rehnquist said his best recollection was that the memo was prepared at Jackson's request and that Jackson did not want or expect clerks to give their own views.

But Jackson's papers, which were not available to the committee at that time, seem to contradict that assertion, showing that Rehnquist and other clerks frequently expressed their views in memos to Jackson.

A related liberal attack may be mounted to question Rehnquist's judicial ethics, focusing on his controversial decision to vote in a case, Laird v. Tatum, involving surveillance of antiwar protesters.

Rehnquist, while in the Justice Department, defended the Nixon administration's surveillance of the antiwar movement during Senate testimony in May 1971. He mentioned the case, then pending in an appeals court, during his testimony, saying he felt it was not "justiciable," that it had no place in court because no one had been hurt by the surveillance.

Months later, when the case came before the Supreme Court, Rehnquist, then a justice, cast the tie-breaking vote as the court ruled, 5 to 4, that the protesters could not challenge the surveillance program in court.

The American Civil Liberties Union had asked Rehnquist to remove himself from the case, but he refused, saying in a published memorandum that he had a "duty to sit" given the closeness of the vote and the need to avoid a deadlocked court, and that the exchange with Sen. Sam J. Ervin (D-N.C.), then chairman of the judiciary panel, was a "discussion of the applicable law," not the particular case.

One of the ACLU lawyers is expected to argue again this week that Rehnquist "was willing to evade and avoid the most basic principles of judicial ethics to make sure the cases turned out . . . to favor his own former 'clients.' "

Those arguments also are not likely to have a significant impact on Rehnquist's confirmation chances. Liberal opponents predict that allegations involving events in Phoenix 25 years ago or 34-year-old memos will hardly dent Rehnquist's reputation as a brilliant jurist.

Liberals say that Rehnquist, at the 1971 hearings, denied allegations that he had harassed voters in Phoenix as a young attorney, but they say the issue must be explored now because no FBI investigation of the charges was conducted and no firsthand witnesses were called.

Rehnquist said then that he considered "indiscriminate use of literacy challenges . . . entirely improper" and added that he spent most of his time at party headquarters, only going to individual precincts "where disputes had arisen in an effort to resolve them."

Other witnesses, however, have said they saw Rehnquist challenging prospective voters in line at minority precincts and serving as part of a "flying squad" of young GOP lawyers and activists dispatched to heavily Democratic neighborhoods. Their charges focused on the 1962 election although some said they saw him challenging voters in the 1964 election as well.

One Phoenix lawyer, who asked not to be named, said that in 1962, he and another Democrat visited a minority precinct as part of a roving patrol to counter GOP efforts.

"We walked up a high flight of steps to a schoolhouse" where Rehnquist and a Republican colleague were standing, the attorney said. "Bill had a camera and he took a picture of us as we came up."

The lawyer said Rehnquist acknowledged he had been taking similar pictures all day. The attorney said they asked whether this amounted to harassment of voters. Rehnquist reportedly laughed and said there was no film in the camera.

The 1971 Judiciary Committee dismissed similar allegations as "wholly unsubstantiated," relying heavily on a letter from Charles L. Hardy, a Phoenix attorney who was then Rehnquist's Democratic counterpart.

Hardy, now a U.S. district court judge in Phoenix, told the committee that he "never observed Mr. Rehnquist attempting to challenge voters at any polling place" in the 1962 election.

In recent interviews with The Washington Post, Hardy said, however, "If someone said he Rehnquist was down there, I couldn't dispute that. I never saw him."

Mirkin, one of the latest to recount the partisan jockeying at the precincts in Phoenix, said he believed firmly that he saw Rehnquist leading the GOP challengers. "I do believe Bill Rehnquist was there, and I told him if he didn't get the hell on out and quit bothering these people, that I would call the sheriff . . . , " he said.

Mirkin added that he believed the Republicans left shortly after the encounter, but "they achieved their purpose just by coming . . . . As I remember it, some people left the polls at that point."

Rehnquist has declined to comment on the latest allegations, but he issued a blanket denial in 1971. He said then that he had never "either myself harassed or intimidated voters, or encouraged or approved the harassment or intimidation of voters by other persons."

Thurmond said last week he expects to hold two days of hearings on the nomination. He said he would "not prohibit" testimony on voter-harassment allegations, but he said it "seems unnecessary."