Colombia's FARC rebels began a 30-day unilateral ceasefire Sunday but there was no let-up from government operations which left one guerilla dead. The Revolutionary Armed Forces of Colombia (FARC) ordered its units to "cease fire and hostilities for 30 days" from December 15 in a message last week from Havana where peace talks to end Latin America's longest running insurgency are being held. President Juan Manuel Santos' government has rejected the idea of any ceasefire until a peace deal has been signed. The government on Sunday said security forces had launched an operation in the southwestern province of Cauca, one of the most restive regions in the insurgency. The government said the offensive killed a FARC fighter believed to be responsible for a bomb attack against a former minister in Bogota last year which claimed the life of his bodyguard and driver. Police said the FARC guerrilla targeted in Sunday's operation had been planning further attacks in Cauca and Bogota. Santos last week said FARC forces would not be shown any respite despite their unilateral ceasefire, saying to do so would give the rebels a strategic advantage. Colombia has endured five decades of conflict that has left hundreds of thousands dead and displaced more than 4.5 million. The FARC -- Colombia's largest and oldest rebel group, which was established in 1964 -- has 7,000 to 8,000 fighters.