Francis made the appeal during his Sunday noon blessing from St Peter's Square.
He said: "I would like to invite you to pray for the dear people of Burundi, which is undergoing a delicate moment: May the Lord help all to avoid violence and act responsibly for the good of the country."
Military and police officials announced a coup Wednesday after weeks of street protests against Burundi President Pierre Nkurunziza's bid for a third term in office.
Soldiers loyal to the president stopped the rebellion.