The petition noted the recently announced resignation of Police Chief Wayne Cleveland and other city officials.
Cleveland announced he would resign as police chief effective Jan. 23 to become the chief in Hopewell, Va.
The petition stated, "We further believe that the mayor is largely responsible for this state of affairs."
Cleveland has declined to answer questions about whether his relationship with Sparks was a factor in his resignation. In his Dec. 21 resignation letter, Cleveland said "bickering" over his resignation would serve no useful purpose.
"I'm not at liberty to say ... I don't know. It's circulating at this point," Anderson said when asked how many people had signed the petition.
"I guess you could say it's symbolic. It's up to the mayor whether he resigns or not," Anderson said.
"It's our way of letting him know he doesn't have the confidence of the voting public," Smith said.
During the meeting, Sparks told Smith and Anderson he would not resign.
The council voted to make Capt. Ted Anderson the temporary police chief when Cleveland leaves.
Councilman Glenville Twigg said the position is being advertised in metropolitan newspapers throughout the mid-Atlantic region and members of the police force also can apply.
Twigg said City Manager Mark Baldwin has been instructed to narrow the list of finalists to not fewer than three nor more than five applicants to be interviewed.
When patrol officers delivered Cleveland's letter of resignation to council members last month, councilman Oden Barrett said some members of his neighborhood were talking about picketing City Hall.
After the meeting, Sparks said that never happened. He added some city employees told him they were going to "make up signs and picket for me" if that happened.
"The way I get it, the campaign is just starting," Twigg said of the petition drive.
"I think it's now up to the people to decide" whether Sparks should remain in office, Barrett said.