They were protesting against the alleged "politicized nature of investigation" into the multi-crore Saradha chit fund scam being conducted by the CBI.
The supporters sat in dharna in front of the office at CGO Complex shouting slogans and holding placards.
"We will continue this sit-in everyday for an indefinite period. We condemn the way CBI is being used intentionally and politically to malign our party and party supremo Mamata Banerjee," Bhattacharya told reporters.
"Now the investigation is being conducted to divert the course of the probe with a political motivation under the influence of BJP government at the Centre. This is nothing but vindictive politics," the minister alleged.
CPI(M) leader Sujan Chakraborty mocked at the TMC's sit-in demonstration outside the CBI office and said they should have demonstrated outside the state secretariat instead.