The civic body staff (safai karamcharis), however, alleged that councillors had attacked them and boycotted work.
Cases have been registered against both parties in this regard, police said.
Varanasi Mayor Ram Gopal Mohle said councillor in Navabganj area, Anil Sharma, and others visited a civic body official, Mahendra Yadav, demanding why garbage was not being picked up from his area.
The issue turned into a heated argument, and the civic body staff members entered into a scuffle with the councillors, Mohle said.
The safai karamcharis have refused to pick up garbage in protest, he said.