IG (headquarters) Jogesh Chatterjee told PTI in Kolkata that a bullet-riddled body identified as one Bharat Mandal, was recovered from Kangra village.
Another person was killed in a separate incident in Nandigram block, he said.
"We are trying to ascertain the identity of the person," he said.
Unconfirmed reports said four persons were killed and ten others injured in indiscriminate use of bombs and shooting incidents at Sonachura and adjoining villages of Nandigram block since Saturday night.
'Bhumi Uchched Birodhi (land eviction resistance)' committee has called a 24-hour bandh at Nandigram today while SUCI has called another bandh in the area on Tuesday in protest against alleged CPI(M) attack on the farmers whose land "was being grabbed" for the proposed industrial project of the Salim group.
The Trinamool Congress headed committee also includes SUCI, Jamaat-e-ulema-e-Hind and naxalite outfits.
The IG said the situation was tense and the police was trying to enter the area.
However, no prohibitory order has been promulgated in the area, he said.
IG (Western range) Arun Gupta has rushed to the spot and reinforcements have been made in the area.
A police picket has been posted in the area, he said.
Meanwhile, Trinamool Congress claimed that the bullet-riddled body, which was recovered from Kangra village was that of a party supporter.
Trinamool Congress MLA Subhendu Adhikary alleged that nine persons were injured as CPI(M) activists attacked villagers at Khejuri village.
Adhikary said that thousands of people blocked the Khejuri-Nandigram road and cut off road links to the area.
The local CPI(M) leaders, however, denied allegations of their involvement in the incident.
CPI(M) District secretariat member Ashok Guria alleged that two party supporters were lynched and another was kidnapped at Nandigram block since Saturday night.