Peres told Francis he has a unique and potentially very helpful role in restarting the dialogue between Israel and the Palestinians, Jewish Telegraphic Agency reported.
"The citizens of Israel see in you a leader of peace and good will," Peres said. "The sooner you visit the better, as in these days a new opportunity is being created for peace and your arrival could contribute significantly to increasing the trust and belief in peace."
The Catholic News Agency reported Francis was pleased to hear of a renewed commitment toward peace in the troubled region home to some of the holiest sites in Islam, Christianity and Judaism.
The Vatican released a statement saying "a speedy resumption of negotiations between Israelis and Palestinians is hoped for."
"So that," it added, "with the courageous decisions and availability of both sides as well as support from the international community, an agreement may be reached that respects the legitimate aspirations of the two peoples, thus decisively contributing to the peace and stability of the region."
The meeting was the first between the newly elected pontiff and an Israeli head of state.
Francis committed to visiting Israel though no date was set.