Civil rights and women's organizations vowed yesterday to ignore the odds and wage an all-out battle to block William H. Rehnquist's confirmation as the 16th chief justice of the United States.

The Senate Judiciary Committee will begin hearings late today, with Rehnquist scheduled as the lead witness. The hearings were to have begun this morning, but were delayed until 4 p.m. to accommodate senators wishing to attend services for the late W. Averell Harriman.

Rehnquist is expected to face prolonged questioning, according to both Senate advocates and opponents of his nomination. The hearings are expected to last through Thursday.

In Phoenix, meanwhile, the FBI is inquiring into recently renewed allegations of voter harassment involving Rehnquist in the late 1950s and early 1960s.

"It's a priority item," an FBI spokesman said yesterday. "If they agents in Phoenix have to work all night, they will."

Organizations opposing Rehnquist's nomination are united under the Leadership Conference on Civil Rights, whose officials assailed Rehnquist in unusually harsh language at a news conference on Capitol Hill yesterday.

Benjamin L. Hooks, chairman of the liberal coalition, denounced Rehnquist as "an extremist . . . an enemy of civil rights" whose rulings in cases involving segregation show a consistent hostility to minorities.

Eleanor Smeal, president of the National Organization for Women, charged that Rehnquist's record on women's rights reflected "a 19th-century view of people." Responding to one question in heated tones, she said it was not Rehnquist's Republicanism that was at issue -- "I testified for Justice Sandy Day O'Connor," she interjected -- but his fundamental views on vital issues.

"He's not just reactionary on our issues," Smeal protested. "It's more than that. It's frightening . . . . He is an advocate of the view that the state can do anything it wants in sex discrimination . . . . His viewpoint is one of unlicensed state behavior. He's a disaster for women."

Despite the vocal opposition, Senate Judiciary Committee Chairman Strom Thurmond (R-S.C.) has said he expects Rehnquist to be confirmed without trouble. The committee's ranking Democrat, Joseph R. Biden Jr. (Del.), has agreed to have the committee vote on the nomination Aug. 14.

A key Republican staff member dismissed the controversy over Rehnquist's role as a Republican activist in Phoenix as "Act One of a liberally orchestrated effort to, at the least, make life miserable for Bill Rehnquist and slow down, if not try to stop, his nomination. At the core of all this is the fact that they don't like the fact that Justice Rehnquist is an unabashedly conservative man, pure and simple."

About half a dozen individuals from Phoenix have said recently that they saw Rehnquist personally challenging black and Hispanic voters in statewide elections, most particularly in 1962. Their statements conflict with a 1971 account by Rehnquist, who said, in response to similar allegations, that he had never "personally engage d in challenging the qualifications of voters."

Sens. Howard M. Metzenbaum (D-Ohio) and Paul Simon (D-Ill.) asked yesterday that all witnesses who might have relevant information about Rehnquist's role as chairman of "ballot security" and similar programs for the Phoenix GOP be asked to testify, it was learned.

Mark Goodin, a spokesman for Thurmond, said the FBI should first be given time to interview these people. "It would seem wise not to put the cart before the horse," Goodin said when asked if they would be called to testify.

Goodin said Thurmond "has approved a routine follow-up by the FBI . . . . They do this all the time. It's as routine as a summer thunderstorm."

In a related development, the Justice Department rebuffed a request from committee Democrats for all records bearing Rehnquist's name as assistant attorney general in charge of the Office of Legal Counsel (OLC) between 1969 and 1971 and dealing with any of four subjects: executive privilege, national security, civil rights and civil liberties, and two of President Richard M. Nixon's Supreme Court nominations.

Assistant Attorney General John R. Bolton, citing attorney-client privilege, said the OLC was "not at liberty to disclose confidential memoranda, opinions and other deliberative materials" concerning its advice to the executive branch.

Opponents of Rehnquist's nomination were asked at yesterday's news conference whether they were upset by the nomination because of the justice's reputation for possessing formidable intellect.

Washington attorney Joseph L. Rauh Jr., one of Rehnquist's chief opponents at the 1971 hearings on his nomination as an associate justice, responded with exasperation.

"Oh sure, he's got a high IQ," Rauh said. "So what? Let them appoint conservative lawyer Roy Cohn. He's got a high IQ. Everyone I know has a high IQ. This man is disqualified for the job because he doesn't believe in individual rights."

Rehnquist, 61, has declined to comment to reporters since his nomination. His opening testimony this afternoon will mark his first public statement since President Reagan ushered him into the White House press room June 17 to announce the nomination.