Under city law, the group has 39 days to collect the required number of signatures of registered voters in order to force a recall election, the newspaper reported Sunday. The newspaper said the deadline could be extended another 30 days if the signatures aren't collected in time.
Filner critics held a "Freedom From Filner" march at 2 p.m. local time Sunday in downtown San Diego, calling for the mayor to step down or face a recall, the Times said.
Meanwhile, Filner supporters scheduled a rally Monday outside City Hall using the slogan "We Will Not Be Silent."
"Bob has stood side by side with many of our displaced communities for decades. Now we stand with him," said border activist Enrique Morones.
Filner has been under fire for allegedly sexually harassing more than a dozen women. Allegations began surfacing more than a month ago and though Filner has been going for treatment, he has said he wouldn't resign.