MOSCOW, MAY 28 -- Rumors of a "pogrom" against Soviet Jews to begin in early June and a series of antisemitic incidents here have frightened Jews in Moscow and other cities.

Jews and non-Jews interviewed here said they have seen threatening, anonymous leaflets tacked up around the city saying that an antisemitic pogrom will begin June 4 -- the date when the Russian Orthodox Church and other churches will officially begin their celebration of the millennium of Christianity in this country. Jewish sources said that many of their gentile neighbors have warned them to stay off the street during the millennium celebration.

The level of fear among Jews, especially in Moscow, is high. "From time to time you hear rumors about various antisemitic acts going on, but the rumors go away, usually," said Tanya Zinman, a Jew who has been refused an exit visa. "But this talk has not gone away. It's everywhere and people are very scared."

In recent weeks there have been incidents of antisemitic vandalism and violence that also have left many Jews bewildered and afraid.

Soviet Jews interviewed here said the current wave of antisemitism is the most ominous in recent memory. One even said he thought this was the worst period of antisemitism in the Soviet Union since 1953, when Joseph Stalin blamed Jewish doctors for his illnesses and Jews in general for countless national problems.

The Soviet government has issued no official statement in response to the reported incidents.

Jewish sources said they were unsure who was behind the leaflets and acts of vandalism. Some suspect ultranationalist, antisemitic groups like the Pamyat organization. Others, including proreform officials, said they thought that enemies of Soviet leader Mikhail Gorbachev, perhaps in the KGB, the Soviet secret police, are sanctioning antisemitic acts to provoke violence that would embarrass the leadership. Still others noted that many Soviets are jealous of Jews who have won a degree of financial success in cooperative businesses, which are beginning to flourish here and in other cities.

Everyone interviewed, however, said that while they supported new government policies of openness, known as glasnost, that very openness has had the ironic effect of clearing the way for antisemites to vent their anger. And while the motivation for these events is obscure, the incidents themselves are frightening.

This month a Jewish cultural group tried to rent the Yauza Club in Moscow to hold an organizational meeting. The club agreed. However, when the group arrived for the meeting, members discovered the doors were locked. The area was surrounded by KGB officers. A handwritten leaflet was plastered to the door.

The leaflet, which was photographed and reproduced by the group, has become a source of particular anxiety among Moscow Jews.

"How long can we tolerate the dirty Jews?" the leaflet said. "Scoundrel Jews are penetrating our society, especially in profitable places. Think about it. How can we allow these dirty ones to make a pile out of our beautiful country? Why {do} we great, intelligent, beautiful Slavs consider it a normal phenomenon to live with Yids among us? . . . How can these dirty, stinking Jews call themselves by such a heroic and proud name as 'Russians?' "

The leaflet was signed "Russia for Russians. The Organization of Death to Yids."

In an area of the Moscow suburbs where many Jews ordinarily rent summer cottages, one house was burned to the ground, sources said. Vandals also broke windows and threw flour and sugar around other homes in suburban towns such as Krosovo.

Jews who would ordinarily go with their families to their cottages in those areas are staying away for fear of possible violence or vandalism.

"We won't go out there until much later in the summer," said Judith Lurye, a prominent Jewish "refusenik," as people rejected for emigration are called. "People don't think it's safe."

The threat of violence against Jews during the millennium celebration, these sources said, is not confined to the capital. In Kiev, militia officers reportedly told the heads of various enterprises to warn workers that "Jewish and Jewish-looking people should not show up on the street" early next month.

Another source said that an Orthodox priest at the Obyedeniya Church in central Moscow gave an antisemitic sermon recently, and letters of protest were sent to church officials.

At Progress Publishers, an official Soviet publishing house, one editor admitted that he was a member of Pamyat and told his fellow workers that Jews risked beatings on June 4. However, the head of Pamyat, Dmitri Vasiliyev, said in an interview that his organization was not organizing any pogroms.

In two official Soviet publications, Moscow News and Vechernaya Moskva, there were reports last week of vandalism in the Jewish section of Moscow's Vostrayakovo Cemetery. Moscow News said that two men from the city of Shakhty -- Communist Party members in Moscow on a business trip -- went on a drinking binge and vandalized 46 tombstones.