Colombia's leftist FARC rebels insisted that US activist Jesse Jackson help mediate the release of a US hostage while the government says it wants the Red Cross only.

Kevin Scott Sutay "is now on the road to freedom. So it would be a shame for a lack of clear thinking to stop Reverend Jackson from leading the mission to get him," a FARC statement warned.

Sutay was captured in June in the central-eastern Colombian region of Guaviare when he traveled through the area as a tourist.

During a visit to Havana, where FARC rebels are negotiating with Colombian government representatives, Jackson said Saturday he would mediate in a bid to help Sutay, his family and the United States.

Jackson, who will be in Cuba until Monday, said he would then head to Colombia.

But President Juan Manuel Santos -- who also rejected the group's request that leftist former senator Piedad Cordoba, who has mediated the release of more than 30 FARC hostages since 2008 -- participate in the mission, wants Red Cross staff only.

Santos said he will not allow "the release to be turned into a show for the media."

It was not immediately clear if either side was prepared to bend to make the American's release happen.

Peace talks between the Revolutionary Armed Forces of Colombia and the government opened last November in Cuba, the fourth attempt since the 1980s to end Latin America's longest-running armed conflict.

In early 2012, the FARC committed unilaterally to stop kidnapping civilians.