Russia's Foreign Ministry said on Tuesday that it is up to the Ministry of Justice to decide whether the country's branch of the Jewish Agency, which helps Jews emigrate to Israel, should be dissolved, and hit out at Israel's stance over the Ukraine conflict.

Relations between the two countries have become strained in recent months, after Israel condemned Russia's invasion of Ukraine and summoned the Russian ambassador over comments made by Foreign Minister Sergei Lavrov.

In an interview on Russian TV, Foreign Ministry spokeswoman Maria Zakharova said that Israel's leadership had taken a biased, anti-Russian stance on the conflict, and dismissed suggestions that her department had a hand in proceedings against the Jewish Agency.

"It's a question for the Ministry of Justice, that's the information I have. It definitely is a legal matter," Zakharova said when asked about the fate of the organization.

"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.

The Ministry of Justice earlier requested the liquidation of the Russian branch of the Agency. Authorities have alleged breaches of privacy laws by the Agency, and are expected to present more details before a Russian court on Thursday.

The remarks appeared to signal an effort by Moscow to distance itself from the case, which has stirred worries in Israel about a crisis with Russia, home to a large Jewish community and the big power with clout in next-door Syria.

Israeli Prime Minister Yair Lapid, who as foreign minister in March condemned Russian actions in Ukraine, said in a statement on Sunday that a closing of the Agency branch would be "grave, with ramifications for (bilateral) relations."

But 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 Agency issue, once Moscow agrees to admits them. As of Tuesday morning, they had not departed. Israel's immigration minister voiced hope they would not prove crucial.

"We will resolve this matter through the diplomatic channel, even if they (delegates) do not go," the minister, Pnina Tamano-Shata, told Ynet TV.

There are 600,000 Russians eligible to immigrate to Israel, she said, adding that there had been a rise in applications since the Russian justice ministry's announcement about the Agency, which is based in Jerusalem and is the world's largest Jewish non-profit organization.