Newly designated Republican National Committee Chairman William J. Bennett signaled yesterday that he is eager to challenge the Democrats on the issue of racial quotas and affirmative action if they make that a battleground issue in the 1992 campaign.

Meeting with a group of reporters, Bennett defended as "perfectly legitimate" a controversial ad that Sen. Jesse Helms (R-N.C.) used on the racial preference issue and said he was prepared to debate the question with anyone "if the Democrats want" to challenge the Bush administration on the issue.

The director of the anti-drug program for the past two years and previously the secretary of education in the Reagan administration, Bennett was identified by White House spokesmen Saturday as the surprise choice to head the Republican National Committee. He will succeed Lee Atwater, who is being treated for a cancerous brain tumor. Atwater is expected to be given a new title as general chairman of the party.

Asserting that he could not discuss his approach to the job until the appointment is made official when President Bush returns from his overseas trip next week, Bennett spoke in vague terms about most policy areas. But when asked about affirmative action and quotas, an issue raised in the Helms campaign and several others this fall, Bennett recalled that he is coauthor of a book, "Counting by Race," which criticized race-sensitive hiring and promotion programs.

"I campaigned for Jesse Helms," he said. Bennett added that it was "perfectly legitimate" for the Helms campaign to run a television commercial that showed the hands of a white worker crumbling a rejection slip for a job which, the ad said, went to someone else "just because he was a minority." The ad, run heavily during the final week of the campaign, was credited by many observers with contributing to Helms's close reelection victory over former Charlotte mayor Harvey Gantt (D), who is black.

Bennett accused critics who said the ad played on racial bias of "muzzling" discussion of affirmative action, adding that he believed "most Americans are troubled" by racial preference programs and "don't believe this is a recipe for improving race relations."

While acknowledging past patterns of discrimination based on race, sex and ethnic background, Bennett said they should not be used to justify hiring or promotion preferences unless there is evidence "the individual involved has been the victim of discrimination. The burden of proof is on the individual," he said.

The same issue arose in Bush's veto of a major civil rights bill this fall and Democrats have vowed to repass the measure in the new Congress. Bennett's comments suggested the administration would welcome such a confrontation.