The UN Security Council agreed on Tuesday that a new UN mission for Colombia could continue to monitor a ceasefire despite a referendum vote rejecting the peace deal.

Colombian President Juan Manuel Santos last week extended a ceasefire with the country's FARC guerillas until December 31 and said he hoped to have a new agreement for peace before that date.

The council "welcomed the parties continued commitment to uphold the ceasefire," Russian Ambassador Vitaly Churkin told reporters following a closed-door meeting.

He said the council had received a request from the parties "for the UN mission to monitor and verify the bilateral ceasefire" and that UN Secretary General Ban Ki-moon would present recommendations on that mechanism.

Council members "encourage the parties and all political actors to continue momentum in the peace effort," said Churkin, who holds this month's council presidency.

In a presentation to the council Jean Arnault, the UN chief of the mission in Colombia, emphasized the country's broad consensus on maintaining the bilateral ceasefire, highlighting the population's dedication to preventing a return to violence.

The victory for the "No" vote in the October 2 referendum was a stunning setback to a nearly four-year effort to end Latin America's last major guerrilla war.

Former President Alvaro Uribe -- who led the main opposition campaign against the peace accord -- said Tuesday he would be willing to meet with the guerrilla group to negotiate an end to the conflict.

The right-wing hardliner had condemned the rejected agreement for letting rebels, even those guilty of gross human rights violations, escape jail time and run for elected office.

Santos launched talks with the Revolutionary Armed Forces of Colombia (FARC) after taking office in 2010, with the two sides sealing a deal on August 24 in Havana to end the conflict, which has claimed 260,000 lives.