* Recent kidnappings could complicate peace talks * Five soldiers killed in combat with FARC in south * Oil sector has been under increasing attacks * Six rebels killed during operations in the north By Helen Murphy and Jack Kimball BOGOTA, Jan 31 (Reuters) - Colombia's FARC rebels on Thursday freed three kidnapped oil contractors, but six guerrillas and five government soldiers were killed across the country as peace talks continued abroad. The kidnappings and other violence came days after the Revolutionary Armed Forces of Colombia, or FARC, made clear during peace negotiations in Cuba that it would continue to capture armed forces, possibly hampering the talks. Under pressure from government forces, the FARC released the workers, who were contracted by Canada's Gran Tierra Energy and were working in south Colombia when they were seized on Wednesday, according to military sources. "They're increasingly weak. They increasingly have to resort to acts demonstrating their weakness, to terrorist acts, and now to kidnappings," President Juan Manuel Santos said. Santos' government and Marxist rebels have been engaged in peace talks in Havana since November, trying to reach an end to a decades-long war that has killed tens of thousands and defied past attempts at resolution. At the start of talks, the FARC declared a two-month unilateral ceasefire, which ended on Jan. 20 with the rebels attacking oil and mining facilities, including two pipelines and a coal-carrying rail line. The government refused to join the ceasefire, calling it a sham by the FARC to gain international attention. The army kept attacking the group and carried out several aerial raids that killed at least 34 guerrillas. Security forces killed six FARC rebels on Thursday, Santos said, in a northern wilderness park that is used to transport drugs. In the southwestern Narino province, also a drug route, FARC guerrillas killed four government troops on Wednesday and in neighboring Putumayo province they killed one soldier, according to the army. KIDNAPPINGS AND INFRASTRUCTURE ATTACKS The FARC, the biggest armed group in Latin America, seized two policemen in the southwest last weekend, the government said. It was the first kidnapping of security forces since April, when rebels released all officials under their control. Chief FARC negotiator Ivan Marquez, one of the group's seven leaders, said on Thursday: "Right now we don't have any official report on that incident, if it was or wasn't the FARC." While the FARC has said it would halt kidnapping to fund its war against the government, it never said it would stop taking members of the armed forces as "prisoners of war." There have been several suspected FARC kidnappings of civilians in recent months, but the group has never claimed responsibility. The government has asked rebels to make it clear they are not wasting time at peace talks in Cuba and genuinely want to end the five-decade conflict. An escalation of hostilities could affect the progress of the peace discussions. Santos has said he wants to achieve an agreement within a year. "We're willing to stay at the table until we find a path that leads us to peace. That's why we said that we will not get up from the table until the desire of the people in Colombia is fulfilled," Marquez told journalists in Havana. The rebels took up arms in 1964 as a Marxist agrarian group fighting social inequality and the concentration of land among a wealthy elite. But they turned to drug-trafficking and kidnapping to finance their activities. Rebels deny this. Since a 2002 U.S.-backed offensive, security has vastly improved in Latin America's fourth-largest oil producer, attracting billions of dollars in investment as explorers pushed into more remote areas in search of crude. But the FARC stepped up attacks on energy and oil infrastructure in 2012. Its bombings of pipelines rose nearly threefold from January to October to 142, though attacks against power transmission towers fell by nearly half in the same period to 35. In the latest incident, Colombia's army said the FARC blew up a transmission tower in a rural zone in the Norte de Santander province on Wednesday.