The police had the information and when they raided the area, Gurung and his group attacked them, the ADG said.
According to reports, assistant Sub-Inspector Amitabh Mallik died of bullet injuries in an early morning operation at a hideout of GJM president Bimal Gurung.
Last night, the police had conducted a raid in the Nimbu Basti area of Darjeeling to catch Bimal Gurung.
Sharma also said they have received information that Bimal Gurung has links with North-East insurgent groups and Maoists.
Meanwhile, the police said that it had intelligence inputs that Gurung was hiding near Patlebas.
Few days back Gurung had told his supporters that he will appear before them on October 30.
ADG Anuj Sharma also said that the attempts to disturb the hills' peace will go in vain since the police is determined to stop the miscreants who would do so, even if it would mean that the lives of the police officials would have to be sacrificed.
Though Union home minister Rajnath Singh appealed to Gurung to withdraw the indefinite strike in Darjeeling, the Centre must now decide if it wants to involve a "fugitive" in the discussions, said an officer in Kolkata, asking not to be named.
Those who fired at the police should be given strict punishment, he said.
Tensions flared in the picturesque hill station of Darjeeling in West Bengal in June when the state government announced it was making the Bengali language mandatory in state schools.
The West Bengal government will do all that is necessary to arrest Gurung, he added.
Gurung, the GJM leader, has been in hiding since August after cases under Unlawful Activities (Prevention) Act were registered against him for his alleged involvement in various bomb blasts in Darjeeling and adjoining areas, reported PTI.
The GJM is an ally of the BJP-led National Democratic Alliance (NDA).