Bogota, Colombia (CNN) -- Colombian rebels and the government are in "exploratory" talks to end the country's nearly 50-year armed conflict, President Juan Manuel Santos said Monday.
Speaking on national TV, the president said military operations would continue alongside any negotiations with the Revolutionary Armed Forces of Colombia, commonly known as the FARC.
The FARC, which has been at war with the Colombian government since the 1960s, is Latin America's oldest insurgency.
"We have developed exploratory talks with the FARC to seek an end to the conflict," said Santos, whose popularity has suffered because of the widespread perception that security has worsened under his leadership.
He vowed to avoid the mistakes of the past.
"Colombians can rest assured that the government is acting with prudence, seriousness and firmness -- always putting first the welfare and peace of all residents," the president said.
Santos invited members of a second rebel group -- the National Liberation Army, or ELN -- to also join in the talks.
Earlier, current and former government sources told CNN that the government and rebels met in Cuba to discuss the possibility of peace.
Present at the discussions, the sources said, were members of the FARC and representatives of Santos. The sources asked to remain anonymous because they were not authorized to discuss the matter with media.
The Venezuelan government was reportedly key to bringing the two sides together, the sources said.
Peace talks between the rebels and the government have occurred sporadically since the 1980s. The last attempt fell apart in 2002. Then-President Andres Pastrana ended negotiations after rebels launched a series of attacks across the country, in an apparent bid to strengthen their position.
Since then, the sides have reached a kind of "hurting stalemate," said Adam Isacson, senior associate at the Washington Office on Latin America.
Though severely weakened in recent years, the FARC continues to carry out kidnappings and attack security forces.
"Neither side thinks they're going to win anytime soon," said Isacson. "What they're looking at is losing thousands more people, with nothing to show for it."
Of course, it remains unclear whether the two sides will reach an agreement at all, and if they do, what that deal might look like.
It's also unclear how much of the FARC the group's leadership would be able to deliver, said Isacson.
The FARC opened the door for talks this year. In a January statement, rebels said they would be interested in addressing certain issues at a "hypothetical negotiating table," calling on the government to address such subjects as privatization, deregulation and environmental degradation.
The statement was signed by the FARC's leader, known as Timoleon Jimenez.
"This conflict will have no solution until our voices are heard. Without lies, Santos, without lies," the statement read.
This spring, the FARC freed the last of 10 government hostages after holding them for more than a decade.
In February, the rebel group said it would also stop kidnapping civilians for money. It did not address the fate of its civilian captives, nor did the group renounce kidnapping for political purposes.
Hundreds of civilians remain prisoners of the guerrilla group throughout Colombia, according to the nonprofit Free Country Foundation.
The United States and European Union consider the FARC a terrorist organization.
CNN's Dana Ford, Marilia Brocchetto and journalist Fernando Ramos contributed to this report.