The State Department yesterday asked Nazi hunter Simon Wiesenthal to accompany President Reagan on his controversial visit next month to the cemetery where Nazi soldiers are buried in Bitburg, West Germany.

Wiesenthal, one of the most celebrated Holocaust survivors, declined. Jewish leaders said he is one of several survivors of Nazi terror in World War II to be asked to join Reagan on the trip to Germany.

The Republican-controlled Senate, meanwhile, called on Reagan to "reassess his itinerary." The nonbinding resolution, sponsored by at least 80 senators and passed by voice vote, said the visit to Germany is "fitting" as "a gesture of reconciliation" 40 years after the German surrender.

Elie Wiesel, a Holocaust survivor and president of the Holocaust Memorial Council, said an administration official approached him about making the trip "about 10 days ago," before Wiesel delivered a White House speech imploring the president not to go. "It was only a stated idea, not a formal invitation," he said.

A prominent Jewish leader here, asking not to be named, said White House officials were "looking for everyone and anyone" who might have been a Nazi victim to join in the Bitburg ceremony and quiet the widespread outcry about it.

The White House spokesman handling inquiries on the Bitburg trip did not return two telephone calls seeking comment.

In a statement today, White House spokesman Larry Speakes said telephone calls starting April 15 were "substantially negative" for the first two days about Reagan's visit. Thereafter, it said, the calls have been evenly divided. However, the White House refused to provide the number of calls, as it did this week when favorable calls were received on Reagan's budget address.

White House chief of staff Donald T. Regan told a group of independent radio network reporters earlier today that Reagan is "anguished" over the controversy. Regan said telephone calls and telegrams were running about 5-to-2 against the cemetery visit.

Reagan has said he agreed to visit the German cemetery at the request of West German Chancellor Helmut Kohl. Kohl wants to dramatize the wartime suffering of all Germans and the strength of the U.S.-West German alliance. Reagan said last week that he considers the German soldiers buried at Bitburg, many of them young draftees, to be victims of Nazism "just as surely as the victims in the concentration camps."

Forty-seven members of Adolf Hitler's Waffen-SS are buried at Bitburg. When American Jewish and veterans groups first protested the visit, Reagan added a stop at the Nazi concentration camp at Bergen-Belsen, but the Bitburg protests continued. On Thursday, 257 House members signed a letter to Kohl urging him to withdraw the invitation to the cemetery.

Wiesenthal, reached by telephone at his home in Vienna, said a U.S. Embassy official there called him today to ask whether he would join Reagan at both Bitburg and Bergen-Belsen. He said he declined.

"This is nothing against the president," he said, "but you must understand my feelings."

Wiesenthal said that he did not know whether any of the Germans buried at Bitburg participated in the murder of Jews and that a check of Bitburg gravestone names for known war criminals turned up nothing.

"But the guards at the camps wore that SS uniform, and I was four and one-half years in the camps," he said.

Wiesenthal said he understood that several other Jewish leaders had refused requests to join the president, but he did not name them.

Rabbi Marvin Hier, dean of the Simon Wiesenthal Center in Los Angeles, decried the White House effort to win public support for the Bitburg visit. "Instead of looking for a way out of it, they are looking for a way to fall even deeper into it," he said.

The Wiesenthal Center, which supports studies of the Holocaust and Wiesenthal's efforts to track down Nazi war criminals still at large, plans to sponsor an alternative ceremony at the American Cemetery in Luxembourg the day Reagan visits the Bitburg cemetery, near the Luxembourg border. Hier said the occasion will commemorate American soldiers who died to end Nazi oppression.

Hyman Bookbinder, Washington representative of the American Jewish Committee, said he did not know of any White House efforts to recruit Jewish escorts for Reagan and considered the matter "a relatively minor aspect of the whole thing."

"What's important is what he does and what he says," Bookbinder said. "We continue to hope that Bitburg will be dropped."

The Senate resolution passed without audible dissent. Although it did not mention Bitburg by name, senators made clear in speeches before the vote that they wanted the Bitburg visit cancelled. They also called on Kohl to relieve Reagan of any obligation to go to the cemetery.

"Chancellor Kohl: Free Ronald Reagan! Let our president go," said Minority Whip Alan Cranston (D-Calif.), who warned of possible damage to relations between the two countries if the controversy persists. He sent a copy of the resolution and transcript of the debate to the West German ambassador here to be sent to Kohl in Bonn.

Several senators said the decision to go to Bitburg was a mistake that is only compounded by refusal to cancel it. "The losses should be cut at the earliest possible moment," said Sen. Arlen Specter (R-Pa.).

Speaking of the resolution, Senate Majority Leader Robert J. Dole (R-Kans.) said, "It's not an effort to jump on the president. It's an expression by the Senate that we should pay tribute to the memory of millions of innocent civilians and allied soldiers who suffered and died at the hands of the Nazis."