The Revolutionary Armed Forces of Colombia, or FARC, captured the Americans on Feb. 13 after their U.S. government plane went down in southern Colombia during an intelligence mission.
"The prisoners of war of the FARC do run the risk of dying as a consequence of a crossfire between members of our guerrilla organization and units of the state security forces, if they attempt to rescue the prisoners by force of arms," said Raul Reyes, a FARC spokesman.
Reyes' comments were delivered in writing to Noticias Uno, a TV news station in Bogota, which broadcast them late Wednesday.
Colombian soldiers, with information from U.S. military personnel, are searching the jungles and mountains of southern Colombia for the three captives.
The Americans work for California Microwave Systems, a unit of Northrop Grumman that provides surveillance systems for the U.S. military, company spokesman Jack Martin said Wednesday.
A fourth American, who also worked for the company, and a Colombian soldier were shot and killed near the scene of the airplane crash.
California Microwave Systems, based in Maryland, specializes in airborne reconnaissance and surveillance systems and ground-based satellite communications systems, but U.S. officials have not divulged the specific mission the Americans were on when their plane went down.
The U.S. State Department has said the United States was not authorizing any negotiations and that military search-and-rescue operations were proceeding.
Washington has provided billions of dollars in aid to Colombia — the third-largest recipient of U.S. assistance after Israel and Egypt — in efforts to wipe out cocaine and heroin production and to help the Colombian government fight rebel groups.
Colombia's war, now in its 38th year, pits the FARC and a smaller rebel group against the government and outlawed paramilitary groups. About 3,500 people, mostly civilians, are killed each year.