The 92-year-old, who served as the ninth president of Israel between 2007 and 2014, reportedly met with the pontiff to discuss a "shared vision for a peaceful future and an end to violence."
Quoted in the Jewish News newspaper, he said: "Unfortunately, since our last meeting, much blood has been spilled in our region and in streets around the world.
"We are witnessing increased terrorist acts against innocent people, and the use of the name of God to murder and kill."
"We cannot remain indifferent to the tens of thousands of refugees, victims and children who have been wounded and have lost family members and their homes.
"We have a moral obligation to our children to stop the hatred and bloodshed."
Pope Francis and Shimon Peres spoke on Monday in a meeting which coincided with World Refugee Day, an initiative organised by the United Nations' Refugee Agency to raise awareness of the plight of the world's 65 million displaced people.
Picture: Yasser Arafat, Shimon Peres and Yitzhak Rabin
Peres was awarded a Nobel Peace Prize for his work with fellow former-Israeli prime minister Yitzhak Rabin and Yasser Arafat from the Palestine Liberation Organisation (PLO) which led to the Oslo Accords being signed between Israel and the PLO.
Peres, who was born in Poland, previously served as head of Israel's navy and director general of the ministry of defence.