"There is no specific threat but we are keeping strong vigil on all the entry and exit points of Kolkata, including the airport, railway stations and bus termini," JCP Jawed Shamim said here.
"Shopping malls, multiplexes and market places are being monitored strongly," he said.
However, former DGP Bhupinder Singh is doubtful of the city's preparedness to meet the challenge in case of a terror strike.
"If attacks can happen in a place like Mumbai where intelligence and the Anti-Terror Squad are very strong, we cannot assure that it won't happen in Kolkata...If any international organisation is involved in an attack then it will become impossible for Kolkata police to take action quickly," he said.
Echoing his views, another former top police officer said the metropolis does not have the infrastructure to tackle a terror attack.
"If a terror attack takes place, it will be a pathetic situation...We neither have the infrastructure nor a well trained force capable of fighting terrorists," the official, who did not wish to be named, said.
Singh, however, said the Kolkata Police had proved their efficiency by cracking the January 2002 American Center terrorist attack case within a short period.
"The people of Kolkata are also very conscious and they have helped the police on numerous occasions. This is an added advantage," he said.