“The rest of world is watching like a movie with popcorn. That’s not acceptable,” Mr. Korniychuk said. Mr. Bennett, he said, was “the first leader from the free world that came to see the leadership of the aggressor. We do appreciate any effort.”

But experts and analysts described Mr. Bennett’s mediation efforts, which came at the request of Mr. Zelensky, as a high-wire act that had only the slimmest chance of success.

“I hope I’m wrong, and I wouldn’t want to criticize the prime minister for trying,” said Martin Indyk, a former American ambassador to Israel and author of a recent book on Henry Kissinger and Middle East diplomacy. “But his chances of success are pretty much between zero and none.”

That, Mr. Indyk said, was not because of Mr. Bennett, but because of Mr. Putin, who appeared “highly unlikely” to be seeking a way out.

Israeli analysts warned that the efforts could end up looking like a fool’s errand or worse.

“Israel has no extra value to offer in mediation efforts; it has no special skills or understanding of this complex situation,” said Ehud Yaari, an Israel-based fellow of the Washington Institute for Near East Policy, adding that this was no job for a “newcomer to foreign policy” like Mr. Bennett, who has been in office for less than a year.

“You can end up with having the Russians, the Ukrainians and the U.S. annoyed with your venture,” Mr. Yaari said.

Mr. Bennett seemed undeterred on Sunday, holding his third phone conversation with Mr. Zelensky since the Kremlin meeting. On the way back from Moscow, Mr. Bennett stopped off for talks and dinner with Chancellor Olaf Scholz of Germany and also spoke by phone with President Emmanuel Macron of France.

Mr. Zelensky and Mr. Korniychuk, the ambassador to Israel, had previously been critical of Mr. Bennett’s efforts to maintain good relations with both Ukraine and Russia, citing sympathy and support for Ukraine’s plight but refusing to supply even defensive military equipment.

Israeli officials said it was essential to preserve good relations with Russia in order to be able to continue Israel’s military campaign against Iranian and Hezbollah entrenchment in Syria, where Russia maintains a significant presence. Israel said it was also loath to take a clear side out of concern for the large Jewish communities in both Russia and Ukraine.

But with the visit to Moscow, Mr. Korniychuk said, “The Israeli government finally took an active position.”

If nothing else, Mr. Bennett’s diplomacy could help Israel, deflecting criticism of its position of remaining on the fence.

In his remarks at the start of his weekly cabinet meeting on Sunday, Mr. Bennett said he could not go into more detail about his meeting with Mr. Putin other than to say that he went “to assist the dialogue between all of the sides, of course with the blessing and encouragement of all players.”

“We have access to all sides and the capability,” Mr. Bennett said. “I see this as our moral obligation to make every effort.”