Havana, Cuba (CNN) -- An American held by Colombian rebels for more than three months will be released "imminently," U.S. civil rights leader Jesse Jackson said Saturday after meeting in Cuba with rebel leaders.
FARC guerrillas captured U.S Army veteran Kevin Scott Sutay on June 20 while he was traveling in Colombia.
Jackson said FARC invited him to Havana, where the group has been holding peace talks with the Colombian government since last October.
"It's a humanitarian gesture of their own volition, demanding nothing in return," Jackson said at a news conference in the Cuban capital. "I consider it as a gesture to reinforce the peace negotiation."
FARC guerrillas said in a statement Saturday they had previously offered to free Sutay but that "the Colombian government did not provide the minimum necessary conditions we need for this procedure."
There was no immediate comment from the U.S. State Department.
Colombian officials previously said they feared FARC would use Sutay's release to garner media coverage.
Jackson said he hopes the Red Cross in Colombia will provide a helicopter to remove Sutay from the remote area of the country where he is being held and that the Colombian government will designate the area a cease-fire zone during his release.
Despite the 10-month old peace talks, the Colombian government has resisted calls for a cease-fire with guerrillas, saying the rebels have used previous cease-fires to strengthen their forces.
Sutay served in the U.S. Army from November 2009 to March 2013. He served in Afghanistan for a year starting in November 2010, according to the U.S. Defense Department.
He is from Willow Spring, North Carolina, and won a number of awards, including an Army Commendation Medal and a National Defense Service Medal. The Pentagon lists his rank as private.
Despite Sutay's military background, Jackson said the Army veteran had peaceful motives for visiting Colombia.
"The fact is, he is a tourist," Jackson said.
FARC, whose name in Spanish is the Revolutionary Armed Forces of Colombia, began fighting the government in the 1960s, making it Latin America's oldest guerrilla force.
There have been sporadic peace talks between the rebels and the government since the 1980s. The last attempt failed in 2002.
CNN's Jessica King and Melissa Gray contributed to this report.