MOSCOW — How many Jews are there in Russia?

With current estimates ranging from 250,000 to more than 3 million people, one might hope that Russia's census, taking place this month, could help answer the question.

But experts and Jewish leaders here warn that Russia's first national head count since the demise of the Soviet Union will likely understate the size of Russian Jewry.

And some Russian Jewish leaders are worried that census numbers could lead some to the conclusion that Russian Jewry is disappearing — which could result in less funding from overseas for Russian Jewish activities.

Results of the census are expected in 2003, but the debate is already on in the Jewish community whether to accept the tally of Russian Jews at face value.

Mikhail Chlenov, president of the Va'ad, a Russian Jewish umbrella organization, admits that any number in the lower range — he expects the number to be around 300,000 — may prove "catastrophic" for many in the community.

"Jewish leaders, especially in the provinces, are already horrified by the result the census will bring," Chlenov said.

The census will count what Jewish demographers term as "core Jews," or those who identify themselves as Jews in interviews.

"What the census will give us is a number of people who are not hesitant to identify themselves with Jews," said Yevgeny Satanovsky, president of the Russian Jewish Congress.

But the actual or potential community is several times bigger, most Jewish leaders say.

Russia's two chief rabbis, Berel Lazar and Adolph Shayevich, said this number could exceed 1 million people.

Satanovsky puts the number even higher — at 3 million.

"This is the number of those who are feeling Jewish or may become Jewish if community outreach is successful," he said.

He pointed out that a survey commissioned this year by his organization revealed that there are 232,000 households in Moscow alone registered under Jewish-sounding names.

Census takers will not ask a question about religion. In Russia, Judaism is generally considered an ethnic characteristic.

The most recent census, conducted in 1989 when the Soviet Union still existed, counted 551,000 Jews within the borders of what two years later became the independent Russian Federation. The entire Jewish population of the Soviet Union stood in 1989 at 1.45 million.

If the estimates given by various experts are to be trusted, Russian Jewry shrunk by about one-half in the past 13 years. Hundreds of thousands of Russian Jews left for Israel, the United States and Germany since the breakup of the USSR, and they are continuing to leave Russia at the rate of about 20,000 people a year.

If the results of the population surveys in Russia and other former Soviet states are to be taken as a true statistical picture, with such a rate of emigration there would now be no Jews at all left in this part of the world.

When the results of this year's census are received, Jewish demographers, sociologists and community leaders will face the difficult task of defining the size of what experts call the "extended Jewish population."

Extended Jewry includes all those who may not identify as Jews in the census but have some Jewish background or attachment to the Jewish community. Some experts believe this population may also include non-Jewish marriage partners of Jews, or even members of households that have Jewish members.

The size of the extended Jewish community, according to most Jewish leaders, stands somewhere between 500,000 and 1.5 million.

Although most Jewish leaders believe the census will undercount the Jewish population, they are nonetheless doing their best to make sure the total is as accurate as possible.

Since the count depends on how many people will declare themselves as Jews, some Jewish leaders were busy in recent weeks calling on their constituencies to do just this.

Some Russians, non-Jews and Jews alike, say they will not participate in the census as a protest. Valery Shapiro, a 63-year-old retired pharmacist in Moscow, is one of them. "I will not participate in the census to protest the very low pension I am getting from the state."

But Shapiro said that if he had to give his information he would not identify himself as a Jew because of deep-seated fears.

"I don't believe the officials when they say all the information will be protected,'' he said.