President Reagan said yesterday that Judge Robert H. Bork "has a decision to make" about whether to withdraw his name from nomination to the Supreme Court, and high-ranking administration officials said they hope Bork will decide to quit now that it is clear he would be rejected by the Senate.

Reagan, briefly answering questions from reporters outside the diplomatic entrance of the White House, said that he would support Bork "all the way" and that "it would be impossible for me to give up in the face of a lynch mob." But when asked whether he would accept whatever decision Bork makes, the president responded, "Obviously, I'd have to."

Sources close to Bork said he intends to make a statement today, but they are not certain whether he will withdraw. They said Bork understands the political realities of his situation but is angry and frustrated that a majority of senators opposes him. Sources said Bork will be honored at a White House rally timed to coincide with Reagan's departure for Camp David today.

Officials at the White House and the Justice Department expressed sympathy for Bork but are in favor of his withdrawing so the administration can submit a new nominee in time for Senate consideration before Thanksgiving recess. "The bottom line is that we need a nine-member court, as quickly as possible," said one official.

The mood at the White House is sour. One official said Reagan is "very angry about the distortions" he attributes to Bork's opponents. Bork was described by friends as being in a similar mood.

"He did not expect when this started out that this would be World War III -- neither did we," said a source close to Bork. The source said Bork "feels that his record was misrepresented and his views distorted."

"He's miserable," another source said. "He's not a politician; he's not used to getting the hell kicked out of him. He can't figure out what happened."

Yesterday the count of senators publicly opposing Bork rose to 53. The new statements came from Sens. Dale Bumpers (D-Ark.), Paul S. Sarbanes (D-Md.), George J. Mitchell (D-Maine), Tom Harkin (D-Iowa) and Daniel K. Inouye (D-Hawaii).

Sens. Ted Stevens (R-Alaska), William S. Cohen (R-Maine) and Ernest F. Hollings (D-S.C.) announced support for Bork.

"Judge Bork will not be confirmed for one simple and profound reason," said Mitchell, who was the 51st senator to announce he would vote against confirmation. "The American people agree with the Supreme Court. They don't agree with Judge Bork."

Justice Department spokesman Terry Eastland said Bork met for about half an hour with Attorney General Edwin Meese III and that "the attorney general is not pressing Judge Bork to stay in or to stay out at this point."

Other officials said both Meese and White House chief of staff Howard H. Baker Jr. have concluded that nothing is to be gained in forcing a Senate vote now that the outcome is clear. But senior officials said Bork also has been counseled by some Senate supporters and conservatives outside the administration not to give up the fight.

One official said that if Bork decides to force a floor fight, Senate Democrats might delay a vote on the next nominee until early next year, when election-year politics could endanger confirmation of a controversial nominee.

"That counsels me to withdraw," the official said.

At the Justice Department, lawyers have begun preparing background material about possible nominees and updating some of the extensive background material that had been gathered in anticipation of earlier vacancies.

"There really isn't a leading candidate," said a department official. "There's no short list." At this stage, the official said, "We are not ready with a name. We need some days to do more research."

White House sources said Baker, a former Senate Republican leader, is committed to "genuine consultation" with the Senate, with the view to getting "at least a distant early warning" of opposition. Baker and Meese held token meetings with senators on Bork after it was clear he was Reagan's choice.

Sources said there is growing Justice Department opposition to nominating Patrick E. Higginbotham, a federal appeals court judge in Dallas. There is also White House opposition to Higginbotham because he is the favorite nominee of several southern Democrats who oppose Bork.

"Right-to-life" groups have started lobbying against Higginbotham, who struck down a Louisiana antiabortion statute, and Higginbotham has written some decisions that are viewed as too tolerant of affirmative action quotas.

Another possible nominee with potential southern appeal is Pasco M. Bowman, a judge on the 8th U.S. Circuit Court of Appeals in Kansas City, who is said to be highly regarded by Assistant Attorneys General William Bradford Reynolds and Charles J. Cooper and by White House aide T. Kenneth Cribb, a former assistant to Meese.

One source who knows Bowman, however, said he has expressed doubts whether the Supreme Court's landmark 1954 desgregation decision, Brown v. Board of Education, could be justified under an original intent approach to constitutional interpretation.

Other names under discussion included 2nd Circuit appeals court Judges Roger J. Miner and Ralph K. Winter Jr.; D.C. Circuit Judges Laurence Silberman and Douglas H. Ginsburg, and 7th Circuit Judge Frank Easterbrook.

Staff writers Edward Walsh, Al Kamen and Bill McAllister contributed to this report.