13 councillors -11 from Congress and two independents - met the CM at his residence and raised their demand.
The councillors, however, said that they did not get a satisfactory answer from the CM.
Independent councillor Sushil Sharma said when Gehlot did not give them an assurance in this regard, they sat on a dharna in a lawn inside the CM's residence for over an hour.
Police and CM residence officials did not confirm whether the councillors staged a dharna after the meeting.
"We have objections to the CEO's functioning style. He never respects and usually misbehaves with public representatives, be it a woman," Sharma said.
"Besides, there are other complaints against him so we demanded his removal. Chief Minister did not assure us so we sat on a dharna inside the residence for one hour and later came out of the place," he claimed.
A Police officer said that the group of councillors was inside the CM's residence to meet the CM and no dharna was staged.