Russia criticised Israel's stance on the war in Ukraine but said on Tuesday that a dispute over a Jewish emigration agency was a legal matter that should not spill over into bilateral ties.
Russia's justice ministry is seeking the liquidation of the Russian branch of the non-profit Jewish Agency, which helps Jews move to Israel.
Authorities have alleged breaches of privacy laws by the agency, and are expected to present more details before a Russian court on Thursday.
"There is no need to politicize this situation and project it onto the entire range of Russian-Israeli relations," Kremlin spokesman Dmitry Peskov said.
"It's necessary to take a careful approach here, but also to realise that all organizations must comply with Russian law."
The case has stirred worries in Israel about a crisis with Russia, which is home to a large Jewish community and wields clout in next-door Syria.
On Tuesday, Israel went public with what it deemed a "one-off" firing by Russian forces at its war planes in May as they struck suspected Iranian targets in Syria.
Peskov and Russian foreign ministry spokeswoman Maria Zakharova both appeared keen to minimise any diplomatic repercussions from the Jewish Agency case.
But Zakharova, in comments to Russian TV, lamented Israel's condemnations of the Ukraine invasion. In May, Israel summoned the Russian ambassador over comments made by Russian Foreign Minister Sergei Lavrov about Adolf Hitler.
"Unfortunately, in recent months we have heard, at the level of statements, completely unconstructive and, most importantly, biased rhetoric from Tel Aviv. It has been completely incomprehensible and strange to us," Zakharova said.
Israeli Prime Minister Yair Lapid has said a closing of the Agency branch would be "grave, with ramifications for (bilateral) relations".
On Tuesday, Lapid's office said that he and Russian President Vladimir Putin had exchanged "written greetings". The office did not immediately expand on that correspondence.
Lapid has put a team of Israeli jurists on standby to fly out to resolve the Jewish Agency issue - once Moscow agrees to admit them. But, as of Tuesday afternoon, they had not departed.
"We will resolve this matter through the diplomatic channel, even if they do not go," Israeli Immigration Minister Pnina Tamano-Shata told Ynet TV.
Some 600,000 Russians are eligible to immigrate to Israel. Tamano-Shata said there had been a rise in applications since the case against the Jewish Agency, which is based in Jerusalem and is the world's largest Jewish non-profit organisation.
At an Israeli conference, Defence Minister Benny Gantz confirmed a TV report that, on May 13, a Russian S-300 air defence battery in Syria had fired at Israeli jets, without hitting any.
"It was a one-off incident," he said.
Israel's coordination with Russia over Syria is "a situation that is stable right now, I think", Gantz added. "But we are always reviewing this story as if we only just began it now."
(Reporting by Dan Williams, editing by Mark Trevelyan and Ed Osmond)
