President Reagan, campaigning for Republican Senate candidate James D. Santini, sought tonight to defuse a growing controversy over nuclear waste here that may cost the GOP political support.

The administration has selected Yucca Mountain in Nevada as one of three possible locations for a nuclear waste depository. The other sites are in Texas and Washington state.

Although a final decision will not be made for several years, the prospect of a local nuclear waste site has touched off protests and political leaders have promised to get Nevada off the list for such a dump. The Las Vegas Sun reported that Reagan refused to meet with Gov. Richard H. Bryan, a Democrat, to discuss the issue during his stopover here. The newspaper said Reagan's popularity has dipped in Nevada since the administration's nuclear dump announcement.

In a speech to a $1,000-a-plate fund-raiser for Santini, who is seeking to replace retiring Republican Sen. Paul Laxalt, Reagan went out of his way to reassure Nevadans on the nuclear issue.

Rep. Harry M. Reid (D-Nev.), a potential Santini rival, announced Tuesday that he would start a statewide campaign urging that letters be written to Reagan opposing Nevada as an atomic dump site.

Reagan, in his speech, attacked those who have made the decision a campaign issue. Promising that the final decision, due in the next decade, "is not and will not be handled in an arbitrary or political fashion," he added:

"What we must do is reject those who would politicize this issue, those who would make political gain for themselves at their country's expense."

Reagan noted that Santini, a former House Democrat who switched parties, had played a role in giving states a veto over nuclear dump locations in their states.

"I will not even be president in 1992 when the final recommendations are expected," Reagan said. "But I can assure you and the people of Nevada: I will never do anything that is not totally safe, and that will be true for any president -- Republican or Democrat -- who follows me."

Noting that Nevada has begun legal efforts to challenge the site selection process, Reagan said the issue is up to the courts and expressed confidence in an "equitable resolution" of the nuclear waste issue.

Reagan flew from here to his California ranch for a five-day vacation.