Nizamuddin, Mithun and Birudon Chakma were abducted yesterday, they said, adding that except for Chakma, who was employed as a driver, the others were manual labourers.
The police said a massive combing operation was launched to secure the release of the three even as it was feared that they were already taken across the border to Bangladesh.
"We suspect the involvement of NLFT and a group of goons belonging to Bru community," a police officer said.
The three were working in the Indo-Bangladesh border fencing works for a construction company and no ransom demand has been received so far, he said.