The statement comes after Russia's Justice Ministry last week requested the "dissolution" of the Jewish Agency because of unspecified legal violations.
The Kremlin has said that a move to close in Russia the agency that processes Jewish immigration to Israel should not be "politicised", calling it a purely legal matter.
"The situation should not be politicised or projected onto the entirety of Russian-Israeli relations," Kremlin spokesman Dmitry Peskov told reporters on Tuesday.
In a surprise move, a Moscow court said last week that the justice ministry had requested the "dissolution" of the Jewish Agency because of unspecified legal violations.
"There are issues from the point of view of complying with Russian law," Peskov said.
"This situation should be treated very carefully," he added, but did not provide further details.
READ MORE: Israel scrambles to halt Russia from shutting Jewish immigration non-profit
A warning shot
Analysts say the move could be a warning shot from the Kremlin towards Israeli Prime Minister Yair Lapid, who has taken a tougher rhetorical line over the Ukraine conflict than his predecessor.
It is also interpreted as an attempt to slow a brain drain from Russia.
Lapid warned Moscow over the weekend that shutting the agency would have "serious" consequences.
A first hearing in the case is due this week.
The agency, established in 1929, played a key role in the creation of the state of Israel in 1948.
It began working in Russia in 1989, two years before the end of the Soviet Union, after which hundreds of thousands of Jews from all over the USSR left for Israel.
More than one million of Israel's 9.4 million residents today have roots in the former Soviet Union.
READ MORE: Israel faces a bigger influx of Russian Jews than Ukrainian Jews