HAVANA (AP) — Colombia's largest rebel group announced an indefinite, unilateral cease-fire Wednesday, saying guerrillas will refrain from staging attacks so long as they aren't targeted by the U.S.-backed military.

The Revolutionary Armed Forces of Colombia made the announcement in Cuba at the end of another round of peace talks aimed at ending Latin America's oldest insurgency.

In a statement signed by the FARC's ruling Secretariat, the rebels expressed hope that the cease-fire beginning at midnight Dec. 20th would "transform into an armistice," and said it would seek the support of several Latin American nations and the international Red Cross to verify its enforcement.

Although the FARC have declared temporary cease-fires before, around Christmas and elections, this would be the first time they've offered to indefinitely lay down their weapons nationwide since the 1980s. The goodwill gesture would appear to add at least symbolic momentum to talks that were strengthened when the rebels last month unilaterally freed an army general two weeks after his surprise capture in a remote part of the country.

But it remains to be seen whether the government will accept the rebels' conditions. In two years of talks, President Juan Manuel Santos' centrist government has steadfastly rejected a two-way truce, fearing the rebels would use the opportunity to rearm as they have in past.

Still, the number of rebel attacks has dwindled notably since 2012, a sign to many that the FARC are negotiating in earnest and an end to a half-century of fighting is within reach.

The two sides have already reached agreements on agrarian reform, political participation for the FARC and how to jointly combat illicit drugs in what was long the world's largest cocaine producer.

But some of the thorniest issues remain unresolved, including how the FARC will lay down their arms and whether commanders will face prosecution for atrocities and drug-trafficking.

Those concerns prompted thousands of Colombians led by powerful former President Alvaro Uribe to march over the weekend in the capital Bogota and other cities to reject a possible amnesty for rebel leaders and demand the government hold them accountable for mass killings, kidnapping and drug trafficking.

Uribe, whose conservative government launched the military offensive credited with pushing the FARC deeper into the jungles, on Wednesday called the guerrillas' conditioning of its cease-fire on the government's withholding of its own firepower a form of "blackmail."

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AP Writer Hannah Dreier contributed to this report from Caracas, Venezuela.