he Soviet news agency Tass tonight quoted President Leonid I. Brezhnev as turning down President Reagan's proposal for a meeting in New York in June and proposing instead a "well-prepared" summit in a third country in October.

The statement was issued after two days of persistent and widespread rumors here that the 75-year-old Soviet leader was near death following his hospitalization March 25. It appeared designed to quash these rumors, reassert his authority and underscore Moscow's continued interest in a dialogue with Washington.

In what Tass described as a "conversation" with an unnamed correspondent of the Communist Party newspaper Pravda, Brezhnev was asked about Reagan's April 5 proposal for a meeting with Brezhnev during a U.N. disarmament conference in New York in June.

Brezhnev was quoted as saying that the proposal had left "a rather vague impression," and then Brezhnev noted that it was he who proposed a summit meeting 14 months ago.

"We are in favor of such meetings now, too," Brezhnev was quoted as saying. "It is understandable that a meeting between the president of the United States and myself must be well prepared and held in a solid way, not incidentally in connection with this or that international forum.

"To be more specific, we are in favor of such a Soviet-American summit meeting that would be in keeping with the lofty responsibility of our states for world affairs and would justify the hopes pinned on it."

"I would say the following considering the time and place of our possible meeting," he continued. It "could be held in some third country, say in Finland or Switzerland . . . . The autumn of this year, for instance October, could be a suitable time for the meetings, to my mind."

Brezhnev was hospitalized March 25 after a strenuous four-day visit to Soviet Central Asia, and well-informed Soviet sources quoted his physicians as saying he would have to convalesce "for weeks." His condition has apparently improved, and he was seen earlier this week entering the same Kremlin hospital and then being driven back to his country home outside Moscow.

An official Soviet statement merely said he was taking his usual "winter rest."

Since March 25, Brezhnev has not appeared in public nor have his photographs been published in the Soviet media. By tradition, he is to be present at a formal celebration of Lenin's birthday on April 22 and again for the May 1 parade.

Brezhnev's "conversation" with the Pravda correspondent, which involved one question and the answer, was the first substantive Soviet statement in the past 24 days.

In recent weeks, no Politburo member has made any policy pronouncements, and top leaders have made only a few public appearances at routine events, giving the impression that the government is at a standstill. At the same time, there were rumors about backstage maneuvering by senior figures positioning themselves for the succession struggle.

Brezhnev's rejection of Reagan's offer for a June meeting was interpreted by some Western diplomats as suggesting that he may not be fully recovered by then for such a taxing foreign visit.

But the Soviet leader's remark about a "rather vague impression" left by Reagan's offer also suggested continued Soviet skepticism about U.S. policies and intentions. Some Soviet sources privately criticized Reagan's "cynicism" in making the offer at a time when Washington had information that the Soviet leader's health had deteriorated and when it was not certain that he would recover.

The Soviets also reportedly viewed Reagan's offer as a device to score propaganda points and were quoted as saying that all previous summits were preceded by painstaking preparations. The last was held in Vienna between Brezhnev and then-president Carter in 1979 when the two men signed the SALT II treaty.

The United States has not ratified the treaty. The Soviet invasion of Afghanistan late in 1979 and the military crackdown in Poland in December have further exacerbated relations between the two countries.

In his remarks to Pravda today, Brezhnev did not specify areas of dialogue with Reagan nor did he set out any conditions for the conduct of the talks.

Moscow's primary concern is Reagan's rearmament program. Senior Soviet officials have told Americans visiting here recently that Reagan was pulling the Soviet Union into a fresh round of the arms race with his increased defense expenditures. They also have pointed out that the new round was focusing on "counterforce" weapons, or the type of heavy missiles capable of delivering a first strike.