SANTIAGO DE CUBA, Cuba - Latin America's longest-running armed conflict may soon end, after both sides in the Colombian conflict announced Wednesday an important breakthrough in peace talks.

In an announcement made in Havana, where both sides have been involved in ongoing mediations, Colombian President Juan Manuel Santos and leaders of the leftist Revolutionary Armed Forces of Colombia, known as the FARC, said they had agreed on a formula to compensate victims and punish those suspected of human rights abuses.

It was the final sticking point in the ongoing peace talks between the two longtime foes.

Announcing the surprise Havana trip on his Twitter account, Santos said, "Peace is near."

Secretary of State John Kerry gave a thumbs up to the development.

"The announcements made today at the peace talks in Havana represent historic progress toward a final peace agreement to end more than 50 years of armed conflict," Kerry said in a statement Wednesday evening. "Peace is now ever closer for the Colombian people and millions of conflict victims."

Santos on Wednesday flew to Havana, where talks have been ongoing for three years, to make the announcement alongside FARC leaders. It was a rare appearance of Santos in the same room with his longtime nemesis.

In one of his few directly political statements while in Cuba, Pope Francis urged both sides of the long-running conflict to reach a deal and end the bloodshed.

"We do not have the right to allow ourselves yet another failure," he said during Sunday Mass at Havana's Revolution Square.

The armed conflict between the FARC and Colombian government forces stretches back to the 1960s and has led to the deaths of more than 200,000 people, mostly civilians.

Contributing: Associated Press