Prime Minister Naftali Bennett spoke with both the Ukrainian and Russian presidents this week in advance of a visit to Israel on Saturday by US Secretary of State Antony Blinken.
Ukraine has spoken of Israel as country that could be a guarantor for a Russian-Ukrainian peace agreement with Russia and its capitol of Jerusalem as a venue for negotiations to end the war.
As part of efforts to pursue peace, Ukrainian President Volodymyr Zelensky said he spoke with Bennett, as well as with British Prime Minister Boris Johnson and Lithuanian President Gitanas Nauseda on Thursday.
"All this is for Russia to understand one thing: it is necessary to seek peace. Russia also needs to seek peace," Zelensky explained in the daily address he has delivered to his people since the start of Russia's invasion of his country on February 24.
Moscow had expected to easily overwhelm its neighboring country, replacing Zelensky's government with a pro-Russian puppet leadership.
Russian forces, however, met stiff resistance that generated heavier losses than anticipated and bogged down its advances.
"If Russia had known it would face that, I’m sure they would have definitely been afraid to come here," Zelensky said.
"With each day of our defense, we are bringing the peace we need so much closer. We are bringing victory closer. Because in this war it is simply impossible for us not to win. And it will be so. And we can't stop even for a minute. Because every minute is about our destiny, about our future. About whether we live or not."
The Ukrainian president has sought help from the international community, calling for humanitarian assistance, arms and the impassion of global sanctions on Russia.
He has also asked for world leaders to help mediate a cease-fire, of which four countries have been most active: Israel, France, Germany, and Turkey. Putin on Wednesday spoke with leaders of all four countries.
Ukraine has spoken numerous times of Jerusalem as a preferred venue to hold a peace summit to end the Russian invasion.
Zelensky's chief-of-staff Andriy Yermak told Israeli reporters in a video call that Israel could also be "one of the guarantors of a major international treaty that would provide clear security guarantees" for his country.
"Such an agreement provides for a large list of countries - potential guarantors. Therefore, we are holding separate consultations with each of these countries in order to meet together afterwards," Yermak said.
Ukraine, he said, "has a very warm, friendly, and special relations with Israel." Yermak said, adding that Ukrainian authorities appreciated Israel's mediation efforts.
"We are amazed at how deeply Israeli officials, including Prime Minister Naftali Bennett, are aware of the issue. And we believe that he is really determined to do everything necessary to bring peace to our land and end the war," Yermak said.
He emphasized, however, that Ukraine would not seek peace at all costs, explaining that there are some compromises that it would not make with respect to independence, territorial integrity, and sovereignty.
Yermak and other Ukrainians have spoken of their frustration at Israel's failure to provide military assistance.