The group, 'Speak Out on FGM', has launched the petition on 'Change.Org' website, and claimed to have received 43,116 signatures till afternoon today.
Female genital mutilation refers to several different harmful practices involving the cutting of the female genitals for non-medical reasons.
In December 2012, the UN General Assembly unanimously voted to work for the elimination of FGM, reckoned as a violation of human rights.
"This is an effort to wipe out this custom from our community. I am happy that thousands of survivors are joining this campaign not only from India, but also from Canada, Australia, South Africa, Britain, etc," A survivor told PTI.
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She said, "At the age of seven, I was subjected to FGM in Mumbai in an unhygienic condition and clandestine manner. The shock and the physical and psychological trauma of that day are still fresh in my mind.
Survivors maintained the reason for the tradition of FGM is to curb sexual drive of women and control them. They claimed FGM has nothing to do with religion and is more of a cultural practice.
According to the World Health Organisation, between 100 million and 140 million women and girls across the world are thought to be living with the consequences of FGM.
"This is the first time that survivors in India have joined hands to publicly campaign against this horrific practice," said Preethi Herman, Country Lead, change.Org.