Updated

A few hours after Colombian President Juan Manuel Santos met privately with his predecessor Alvaro Uribe, who led opposition to the now doomed deal with the FARC, thousands of people marched through the capital demanding that the government and leftist rebels not give up on a peace deal narrowly rejected by voters on Sunday's referendum.

Santos and Uribe talked privately for several hours, accompanied by aides, announcing only that they agreed to form a commission that will begin meeting Thursday to evaluate ways to improve the accord.

The "March for Peace" was organized on social media by student groups and social movements that were on the losing end in Sunday's national referendum. Many walked silently, while some carried pictures of loved ones among the 220,000 killed during the half-century conflict involving the military, leftist rebels and right-wing militias.

"We're very close to achieving peace, a stable and lasting peace with broader popular support," Santos said in a statement after meeting with Uribe, who governed from 2002 to 2010.

To save the accord, Santos ordered his negotiators to return to Cuba on Monday to consult with FARC leaders who watched the results come in from the communist island. On Wednesday, the Obama administration sent a special envoy to Havana as well.

Although FARC leaders have said they have no intention of returning to the battlefield, and have been encouraging Colombians to make their voices in support of peace be heard, it's not clear they are willing to reopen talks. If they do, Uribe will almost certainly push for stiffer penalties.

FARC commander Timochenko on Tuesday said the referendum results have "no legal effect whatsoever," citing the fact that the "final" accord had already been signed and deposited with the Swiss Federal Council in Bern as a special humanitarian agreement under the Geneva Conventions.

The parties agreed to create several committees to discuss sections of the peace deal that its opponents reject and make progress toward a solution.

Santos, who served as defense minister under Uribe but has been the target of his predecessor's verbal attacks since taking office and pursuing a peace process with the Revolutionary Armed Forces of Colombia, or FARC, guerrilla group, said he was determined to find a path to not only wrapping up a new agreement with the rebels but making it even stronger.

"We listened attentively for more than four hours to their concerns," Santos said of his talks with Uribe and other members of his Democratic Center party, including erstwhile presidential candidates Oscar Ivan Zuluaga and Marta Lucia Ramirez.

Santos met hours earlier with another opponent of the peace deal - former President Andres Pastrana, who governed from 1998 to 2002 -, thanking him afterward for "his generous attitude and willingness to help safeguard the process at this historic moment."

Santos, who on Sunday night recognized the "no" vote's narrow victory by a margin of 50.21 percent to 49.78 percent, said Tuesday night that a new bilateral cease-fire had been decreed with the FARC and would expire on Oct. 31.

Political marches are rare in Colombia, a reflection in part of an elite-driven political system that fueled apathy and left many Colombians marginalized. Turnout for Sunday's referendum was barely 37 percent — less than many congressional elections.

"We need peace no matter what it takes," said Jennifer Lopez, a 28-year-old teacher who said a cousin had been kidnapped years ago by the FARC. "The meeting between Santos and Uribe shouldn't have been behind closed doors. All the Colombian people should know what they're deciding."

Based on reporting by the Associated Press and EFE.

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