About 25,000 Jews live in Iran, with 15,000 living in the capital of Tehran, where they are safe as long as they do not engage in pro-Israeli politics or spy activities.
In 1999, 13 Jews were accused of spying for Israel. Ten eventually served jail terms, with the last being released in 2002.
The existence of the Iranian Jewish community has come under the spotlight with the appearance of a 15-member women's amateur folk dance group that came to Moscow last week to take part in the Light a Candle Jewish children's arts festival.
"We have not had any contacts with Iranian Jews," said Adolph Shayevich, one of Russia's two chief rabbis. "We have heard various rumors lately, that there is no Jewish community in Iran, that things are bad for Jews there. We are happy to see it for ourselves that this isn't the whole truth."
The Iranians -- aged 14 to 30 -- came to Russia thanks to diplomatic efforts by Arkady Gaidamak, a Russian Jewish leader and businessman, and with a special permit from the Iranian authorities.
Russia is a major supplier of nuclear technology to Iran, which is currently under strong international pressure to halt its supposed nuclear weapons program.
In addition to general tourist sites, the delegation visited a synagogue and a Jewish day school in Moscow, as well as the Jewish community of Yaroslavl.
But the Jewish women who visited Russia said their community has a future in Iran -- despite the militant anti-Zionism of Tehran's current political regime.
"After the revolution, problems began for the community," said Elham Abaei, 30, the leader of the group that came to Russia.
Abaei, who runs the Iranian Jewish community's Web site, www.iranjewish.com, said the community has adjusted to the political and social climate.
"We can now run cultural and religious but not political activities," she said, referring to anything related to Israel.
Most recently, Iran's president, Mahmoud Ahmadinejad, caused a wave of international condemnation when he suggested that Israel should disappear from the map and called the Holocaust was a myth.
The statement about the Holocaust reportedly triggered a rare example of discontent from the country's Jewish leadership. Yeshayaie, the community's chairman, wrote a letter to Ahmadinejad saying that the remarks caused fear in the country's Jewish community.
But on the issue of Israel, these Iranian Jews would not speak out against Tehran's official policy. "You can be Jewish and not associate yourself with Israel," said Sarah Hay, a 21-year-old computer engineering student from Tehran.
Even far away from Tehran, members of the group tried to distance themselves from any reference to Israel when visiting Russian Jewish institutions.
In Yaroslavl, a city in central Russia, the local community baked two cakes for the Iranian guests.
But members of the group were visibly shocked when they saw the cakes were glazed with the design of the Israeli flag. The hosts gave the guests only those slices of cake without the flag design.
The communal activities range from Jewish day schools -- one-half of Tehran's Jewish children are said to attend Jewish day schools -- to synagogues, youth clubs and summer camps, and even a Jewish hospital in Tehran.
One of the members of the group described her community as one having "everything a Jewish community should have" except for any Israeli connection.
Iranian Jews are accorded a status of an officially recognized minority and are free from discrimination. "We are Iranians first, we share our country's history," Hay said. "There are no ghettos, you can live your life," she said.
She said some Jews "were slightly offended" over Iranian president's remarks about the Holocaust. But years of state-run propaganda show themselves in the Jewish community members, and one said some Jews may disagree that the Holocaust was a myth, yet they are inclined to think the number of Jewish Nazi victims may be "an exaggeration."
A Moscow Jewish leader said the Russian community should take advantage of Moscow's good relations with Tehran to benefit Iran's Jews.
"Maybe we can invite a group of Iranian Jewish boys to study in a Moscow yeshiva," said Pinchas Goldschmidt, Moscow's chief rabbi.