The dramatic claims were made on the group's official website which also said the kidnap was organised to coincide with the 30th anniversary of Chilean president Salvador Allende.
The tourists were forcibly taken in the jungles of the northern Sierra nevada mountains on 12 September.
A statement on the website read: “The National Liberation Army takes responsibility for the operation Allende Lives, marking the 30th anniversary of his death."
Chilean president Salvador Allende committed suicide on the same date in 1973, during a military coup led by General Augustine Pinochet.
The communist group said it had the “will to find a peaceful solution to this operation” and that it seeks peace with social justice.
“Our side is disposed to talks and the search for the best outcome,” the Internet communiqué added.
The ELN also rejected accusations that it is a 'terrorist group' saying that “the assassins of Allende were the real terrorists. The imperialists and the far right. Those in the White House [are terrorists]. Yesterday it was Pinochet. Today it is Ariel Sharon, Tony Blair, Jose Maria Aznar and Alvaro Uribe in Colombia.”
"Our side is disposed to talks and the search for the best outcome"
ELN Internet communique
President Alvaro Uribe on Friday urged the group to free the seven remaining hostages after 19-year-old Briton, Matthew Scott, escaped, living 12-days in the jungles of the northern Sierra Nevada mountains before being found by local tribesmen.
“We call on the ELN to free these people - which would be good for Colombia and the world - and to sit down at the negotiating table,” the president told Caracol Radio.
The ELN is the smaller of Colombia's two main rebel groups, with 4500 armed paramilitary members. The Revolutionary Armed Forces of Colombia (FARC) has some 17,000 fighters and politically Marxist.
“The FARC influences the ELN and is an obstacle to moving forward,” he said. “It is better for the ELN to make use of ballots, not bullets.”
Gunmen seized the tourists on September 12 as they wandered through the ruins of the 3500-year-old Lost City, located some 950 km north of Bogota in an area known for its lawlessness.
Still believed captive are Briton Mark Henderson, German Reinhilt Weigel, Spaniard Asier Huegun and four Israelis, Beni Daniel, Ortaz Ohayon, Ido Joseph Guy and Erez Altawil.