Sen. Joseph R. Biden Jr. (D-Del.), chairman of the Senate Judiciary Committee, announced yesterday that he is almost certain to oppose the nomination of U.S. Appeals Court Judge Robert H. Bork to the Supreme Court and said hearings on the nomination will not begin until Sept. 15.

Biden, in saying there is "an overwhelming prospect" that he will vote against Bork, also signaled a likely liberal Democratic theme on the issue, portraying the jurist as an ideological tool of President Reagan, Attorney General Edwin Meese III and other administration conservatives.

"Quite frankly, it goes well beyond Judge Bork," Biden said. "It's a question of whether the Reagan-Meese agenda is going to be accomplished through the court and whether Judge Bork has been picked to be the vehicle to accomplish that."

Biden made the comments after he and the seven other Democrats on the Judiciary Committee agreed to the Sept. 15 date, virtually assuring that Bork's nomination will not be settled when the Supreme Court begins its term on Oct. 5.

Biden, who said he expected to issue a formal statement on Bork in about 10 days, added that the confirmation fight will be "the most significant debate not only on the future of the court but on the social and economic agenda" of the country.

In a private meeting in his office earlier, Biden promised civil rights lobbyists that he will lead the opposition to Bork and make the fight his top priority, according to knowledgeable sources. Biden told the activists, whose constituencies are important to his presidential campaign, that he will detail his reasons for opposing Bork in his upcoming statement, the sources said.

Representatives of the Leadership Conference on Civil Rights, Alliance for Justice, NAACP Legal Defense and Education Fund and the Women's Legal Defense Fund attended the meeting with Biden. The groups would not discuss the meeting yesterday.

Senate Minority Leader Robert J. Dole (R-Kan.) strongly objected to the Sept. 15 date, asserting that "there is absolutely no substantive reason why we have to wait more than two months to begin the nomination hearings." He said Judiciary Committee Republicans "are willing to stay here during the August recess {scheduled Aug. 8-Sept. 8} if necessary" to expedite the nomination process.

Dole said he hoped to meet with Biden, Majority Leader Robert C. Byrd (D-W.Va.) and Sen. Strom Thurmond (R-S.C.), ranking Republican on the Judiciary Committee, as Senate Republicans seek to extract concessions from the Democratic majority on the timing and pace of the nomination debate.

Mark Goodin, a spokesman for Thurmond, said Thurmond did not object to Sept. 15 provided agreement is reached on several other aspects of the confirmation process.

Most important is a written agreement Thurmond is seeking for a "reasonable time certain for a vote in the committee," clearing the nomination for debate on the Senate floor, Goodin said.

Thurmond said earlier he hoped the committee would complete action on Bork by late September, but that appeared unlikely. Biden promised yesterday that there will be "no delay," but estimated the hearings would take about two weeks.

Sen. Patrick J. Leahy (D-Vt.), another Judiciary Committee member, added, "If all the mail I've received from the little state of Vermont is any indication, I don't see how we could complete the hearings in two weeks."

The written agreement that Thurmond is seeking is similar to an accord reached last year when the Senate considered the nomination of Justice Antonin Scalia and the elevation of Justice William H. Rehnquist to be chief justice. But last year the Republicans controlled the Senate. Biden, speaking yesterday for the new Democratic majority on the Judiciary Committee, said there is "no inclination to set any end point" for the deliberations.

Underscoring the importance of the confirmation battle, Biden said, "This is probably the most significant Supreme Court nomination of the last several decades and arguably of the century."

The Judiciary Committee is sharply divided along ideological lines and the committee's vote on the Bork nomination is expected to be close. Biden said, however, that even if the committee votes against the nomination, the issue will be brought to the Senate floor.

Biden has been under pressure from liberal activists, who had criticized his delay in opposing Rehnquist, to attack Bork. Biden, who said last fall that he would probably support a Bork nomination and would not be pressured to do otherwise, has since said Bork would tip the court's balance too far to the right.