Colombian President Juan Manuel Santos and opposition leader Alvaro Uribe were unable to find common ground on a peace accord with Marxist FARC rebels, even with the mediation of Pope Francis when they met at the Vatican on Friday.

On his third visit to the Vatican, Santos appealed to Francis for support in ending a 52-year war that has killed more than 220,000 people and displaced millions.

"We need your help," said Santos, who signed a modified peace deal in November after a previous pact was rejected in a plebiscite. He gave the pope a gift of a pen made from a machine gun bullet.

Francis, an Argentine who has helped broker diplomatic efforts in Cuba and Venezuela, then received Uribe, a right-wing senator and former president who has been one of the harshest critics of the new peace deal.

The former allies also met Francis together for around 20 minutes. A photograph released by the Vatican showed them sitting side by side at a table in the pope's private study. It appears no consensus was reached.

"I told ex-president Uribe that we are always ready, as we have said in previous occasions, to continue dialogue, to reach agreement about how the peace accord should be implemented," Santos said after the joint meeting.

Uribe argues the new deal is not tough enough on Revolutionary Armed Forces of Colombia (FARC) rebels since it does not include opposition demands that they serve traditional jail sentences and be barred from forming political parties.

"If the government allows room to examine certain issues, we could look for options," Uribe said, reiterating a previous demand.

Santos won this year's Nobel Peace Prize for his efforts to reach an accord, under which some 7,000 rebels are now heading to special demobilization areas to hand in their weapons.

Francis has repeatedly expressed support for the deal over four years of negotiations. At Friday's meeting, he presented Santos with a medal and copies of the three encyclicals produced during his papacy.