The clash took place on Sunday night in Burdwan district's Khandaghosh area.
While police have refused to comment on political allegiance of the victims, Trinamool's block president Alok Manjhi accused local party leader Muzzam Hussain Mani of being behind the killings.
"Three people have been killed in the clash. We are probing the matter and cannot comment right now if the killings were a result of an internal clash between the Trinamool factions. We have detained six people," Additional Superintendent of Police Tarun Haldar said.
Manjhi said: "Ever since Mani was removed as the block president, he has been looking to take revenge. Last night his men dragged three of our people and mercilessly killed them."
"We have filed a police complaint and demand exemplary punishment for this."