BOGOTA (Reuters) - Civil rights activist Jesse Jackson urged Colombia's FARC rebels to free a former U.S. Marine they kidnapped in June as he hiked in the jungle, saying the move would help peace talks between the guerrillas and the government.

Kevin Scott Sutay, a veteran of the war in Afghanistan, was captured by the FARC after being warned by police not to trek through what they called a hazardous "red zone" for rebel activity. He had been backpacking through Central America and South American countries.

Kidnappings were once common in Colombia until the FARC, or Revolutionary Armed Forces of Colombia, pledged last year to end kidnapping for ransom, but reserved the right to take war prisoners.

"If anyone in the jungle hears this message, please tell his captors that when prisoners are liberated, a door always opens for dialogue," Jackson said. He was attending an international conference of Afro-descendent mayors and government officials in Cartagena on Colombia's Caribbean coast.

"It would be a stimulus for the peace process in Cuba if we could achieve this liberation," said Jackson, referring to talks between the Colombian government and FARC that began last year in Havana and have proceeded slowly.

The FARC looked ready to release Sutay to the International Committee of the Red Cross in July, but hardened its stance after President Juan Manuel Santos refused some of their conditions and said he would not let the FARC make an ostentatious "media show" of the event.

The rebels then began accusing Sutay of having come to the country as a mercenary. The FARC has made no further mention of plans to release him.

The left-wing FARC and their smaller counterpart, the National Liberation Army, have been trying to overthrow the government of the Andean nation for five decades.

The FARC's ranks have been halved to about 8,000 fighters by a decade-long U.S.-backed government offensive, but its continued deadly attacks against the armed forces and country's infrastructure show it is still a force to be reckoned with.

(Reporting by Julia Symmes Cobb and Peter Murphy; Editing by Daniel Wallis and Stacey Joyce)