"Conscious of the numerous obstacles that remain to be overcome, we hope our meeting contributes to the re- establishment of this unity wished for by God," they said in a joint declaration yesterday.
They signed the declaration after holding talks in Cuba, the first such meeting between the leaders of the Eastern and Western churches in nearly a thousand years.
"We call on the international community to take urgent action to prevent Christians from continuing to be driven out of the Middle East," they said.
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.
The Argentine pontiff was looking to heal a nearly 1,000- year-old rift in Christianity that dates back to a 1054 schism that helped shape modern Europe and the Middle East.
Francis is now due to embark on a tour of Mexico, while Kirill continues a visit to Cuba, Brazil and Paraguay.