The campaign, dubbed the "Right to Pee" campaign, is led by 35 non-government organisations (NGOs), and urges women in Mumbai's civic authority to ensure that the service is free for women.
Women currently make up 50% of Mumbai's civic authority.
Rahul Gaekward, who heads one of the 35 NGOs in the campaign, has outlined three basic requirements for women.
"They should be allowed to pee for free, the public toilets should provide vending machines with sanitary towels, like men have for condoms, and they should have a changing room in the toilets," he said.
There is an acute shortage of both public and private toilets in India, and public defecation is common across the country.
A census in March found that half of India's homes do not have toilets.
The campaign is drawing a strong response from both men and women.
One man who signed the petition told the BBC he wanted better facilities for women in all public toilets in the city.
According to Mr Gaekward, more than 7,000 signatures were collected in the crowded and impoverished Kurla area last week.
A female student who signed the petition in the middle-class Dadar suburb said it was a question of dignity for women.
"We face a lot of problems because there are inadequate facilities in the city's public toilets," she said.
The campaigners say they surveyed 129 public toilets last year and found that the facilities for women were woefully inadequate.
They launched the same campaign last year, but received no response from the civic authority.
This time round the campaigners want to confront the female members of the authority after collecting as many signatures as possible.