There is no deadline for agreement, though Santos has said he expects results in months, not years, or he will halt the negotations.
The talks, the result of seven months of secret negotiations in Havana, follow four failed efforts since the early 1980s.
A cease-fire reach with the FARC in the first of those efforts fell apart amid accusations of mutual failures to honor it.
Universidad de los Andes political scientist Sandra Borda said in Bogota that the rebels' cease-fire announcement has her wondering whether the FARC's leadership can pull it off.
"If it works, it will substantially change the tone of these negotiations," said Borda, and become "a mechanism of pressure on the government to stay at the table."
Land reform, the heart of the conflict, is at the top of the agenda and the negotiators vowed in a roadmap agreement signed Aug. 26 that both sides would keep the negotiations secret pending joint public progress reports.
The Colombian government is hoping peace leads to greater foreign investment, including the extractive industries, and says its economic model is not negotiable. But the FARC is insisting on nationalizing natural resources.
The government has promised to return millions of acres of stolen land to displaced peasants, one of the rebels' main demands, and compensate victims.
The 9,000-strong FARC is being asked as a condition of peace to help end the cocaine trade that has funded its struggle.
Colombians also want it to account for the dozens of kidnap victims who have disappeared in its custody and other noncombatants it is accused of killing.
Paul Haven in Havana, Cesar Garcia and Vivian Sequera in Bogota, Colombia, and Frank Bajak in Lima, Peru, contributed to this report.
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