"For nearly one thousand years, Catholics and Orthodox have been deprived of communion in the Eucharist," they said in a joint declaration signed after talks in Cuba.
"We are pained by the loss of unity, the outcome of human weakness and of sin."
It was the first meeting between the heads of the Russian orthodox and Western churches since the great schism of 1054 when the churches split apart, with the Eastern church rejecting the authority of Rome.
"Mindful of the permanence of many obstacles, it is our hope that our meeting may contribute to the re-establishment of this unity willed by God," the church leaders said.
Their meeting was driven by rising violence in recent years in the Middle East, where Christian communities have suffered violence at the hands of extremists.
"We call upon the international community to act urgently in order to prevent the further expulsion of Christians from the Middle East," they said. "In many countries of the Middle East and North Africa whole families, villages and cities of our brothers and sisters in Christ are being completely exterminated," they went on.
"We wish to express our compassion for the suffering experienced by the faithful of other religious traditions who have also become victims of civil war, chaos and terrorist violence."
The 79-year-old Francis, in white robes and a skullcap, and Kirill, 69, in black robes and a white headdress, earlier
kissed and embraced before sitting down smiling for the historic meeting at Havana airport.
Between them, they are the spiritual leaders of more than 1.3 billion Christians.
"At last we meet. We are brothers," said the pope as he met the white-bearded Orthodox leader. "Clearly, this meeting is God's will."