Though no date was mentioned, the president told journalists, the Pope said a peace agreement would be a "determining factor" for a papal trip to the beleaguered Latin American country.
Santos' government has been holding peace talks with the Revolutionary Armed Forces of Colombia (FARC) Cuba since 2012. But an end to more than five decades of conflict, which has killed at least 220,000 people and terrorized countless citizens, still seems far off.
Less than a week before the Pope's meeting with Santos, the 7,000-member guerilla group killed several police officers in Colombia, bombed electricity towers and emptied crude oil into a river, cutting power and clean water supplies to hundreds of thousands of people.
After 20 minutes of private discussions between the Pope and Santos, Vatican journalists were permitted to observe the rest of the meeting, held in the Pope's private library.
"You are the person for whom I've prayed the most for the peace process," the Pope told Santos. "And I pray for this."
"This is why I am here, to ask for your help," Santos replied.
After the meeting, Santos met with journalists and said the Pope told him he was available to help in the peace process in Colombia. However, the Pope did not mention direct mediation, said Santos.
"The Holy Father told me: 'If you need us to play a role, we are ready to do so,' something that pleases us, because he is currently ... the most authoritative voice in the world," he said.
Pope Francis also emphasized the importance of dialogue and reconciliation for all Colombians, Santos said.
The president said he also sought counsel from the Pope on how the victims of violence can be helped. The Pope replied that the church would be available to help in the process with victims as well, Santos added.
The two leaders also spoke about the pontiff's upcoming encyclical on the environment, "Laudato Si'," and the importance of the environment for the livelihood of the Colombian people, said Santos. The Colombian president told the Pope the ongoing conflict with the guerillas has been ruinous for his country's environment. In addition to the oil spill in early June, the president mentioned the impact of narcotics trafficking on the tropical forests.
For the customary exchange of gifts, the pontiff gave Santos a bronze medal of St. Martin of Tours, as well as a copy of his apostolic exhortation, "The Joy of the Gospel." The Pope said the bronze medal is a gift he likes to give government leaders as a reminder for them to "protect the poor." In response, Santos told the Pope that, among Latin American countries, poverty has dropped most in Colombia in the past four years.
Santos gave the Pope eight place settings of hand-crafted dinnerware, as well as a large Colombian flag with a dove on it, a flag he created when the peace talks began. The Pope blessed a smaller version of the flag, which Santos reportedly keeps on his desk.