"Meeting of delegates and advisers to Government and FARC in Havana. Starting constructive dialogue. Let's get peace done," the government side said on Twitter.
"It's an optimistic atmosphere. Let's get peace," the lead FARC negotiator Timoleon Jimenez (Timochenko) tweeted.
The sides are "trying to find common ground," he said.
Santos -- who has staked his legacy on making peace -- had extended the army's ceasefire to December 31 if no solution to the impasse is found by then.
The FARC, which had criticized Santos's deadline, has also confirmed its willingness to continue negotiations and maintain a bilateral ceasefire.
The Colombian leader won the Nobel Peace Prize just a few days after voters shot down the historic accord in a referendum that would have ended more than 52 years of conflict.
Since the accord's rejection on October 2, Santos has held marathon talks with political figures including the country's former president Alvaro Uribe -- who led opposition to the agreement -- as well as religious leaders and victims of the armed conflict.
Under the peace accord that was rejected in the referendum, the FARC's estimated 7,500 fighters are to disarm under UN supervision.
Santos launched talks with the Revolutionary Armed Forces of Colombia (FARC) after taking office in 2010, with the two sides sealing a historic deal on August 24 to end the conflict, which has claimed 260,000 lives.
But there is no ceasefire in place with the much smaller National Liberation Army (ELN).
The FARC and ELN have been at war with the state since 1964.
The ELN is estimated to be about a quarter the size of the FARC, with some 1,500 fighters.