In a statement faxed to Reuters on Monday bearing no insignia or letterhead, the group calling itself Strugglers for the Unity and Freedom of the Levant, said the same fate awaited other opponents of "Arabism" in Lebanon.
There was no way to verify the authenticity of the statement, whose wording appeared designed to cast suspicion on Damascus, which is ruled by the Arab nationalist Baath party.
Syria ended its 29-year military presence in its smaller neighbour in April after the killing in February of former Lebanese prime minister Rafiq al-Hariri.
The statement read: "We have broken the pen of Jebran Tueni and shut his mouth forever and transformed Al-Nahar into a very dark night."
Al-Nahar means "The Daytime."
"We have succeeded today again in liquidating another of the mouthpieces that have ... spread their poison and lies and not stopped despite the warnings we have sent him time and again."
Some Lebanese politicians have blamed Syria for Tueni's death, but Damascus denied any role, saying the killing was timed to smear it.