Yatsenyuk said he asked Francis "to pray for Ukraine and for stability in Europe" and told him he was grateful for the support.
He said the Vatican had already averted wars during the Cuban Missile Crisis in 1962 and the Argentina-Chile territorial dispute in 1978.
The Vatican said in a statement that Francis and Yatsenyuk had discussed the "specific role" that religious organisations could play "in fostering mutual respect and harmony".
"Mention was made of possible further initiatives by the international community in this regard," the statement said.
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Yatsenyuk spent 18 minutes behind closed doors with the pope, who had urged the international community to "prevent violence" in Ukraine in his Easter Sunday message.
At an exchange of gifts, Yatsenyuk presented Francis with a photograph of Maidan square in Kiev on New Year's night.
"This is where Ukrainians fought for their freedom and rights. Millions of people," he said.