The group, known as the ELN, did not make any demands in its statement, but said it was open to negotiations "to find a solution."
The Cuban-inspired ELN, which along with the FARC has been battling the Colombian government for four decades, condemned the massive military operation underway to hunt for the kidnapped tourists, warning President Alvaro Uribe that he will be to blame if the hostages are harmed.
"In the case of lamentable acts that could occur because of the presence, or the actions, of the army and paramilitary groups in the area, President Uribe would be held personally responsible."
The group of eight backpackers - four Israelis, two Britons, a German and a Spaniard - was abducted by gunmen on Sept. 12 from the Lost City archaeological ruins in the snowcapped Sierra Nevada mountains. One of the Britons, 19-year-old Matthew Scott, escaped days later by hurling himself down a precipice.
The Revolutionary Armed Forces of Colombia, or FARC, the biggest left-wing rebel group, was initially blamed, but it denied involvement. On Friday, President Alvaro Uribe accused the ELN and demanded it set the backpackers free.
In its statement Monday, the ELN said the hostages were taken in an operation they dubbed "Allende Lives," timed to mark the 30th anniversary of the coup in Chile that overthrew the government of President Salvador Allende, a Marxist.
The ELN urged the United Nations to visit the Sierra Nevada mountains to see firsthand the plight of impoverished inhabitants there.
The kidnapping was a setback in the all-out war that Uribe has launched against both rebel groups with the help of millions of dollars in military aid from the U.S. government. On Monday, Uribe is due to travel to Washington to secure pledges for continued military aid.
By Vanessa Arrington