Over 100 activists from the northern region gathered at Jantar Mantar here and staged a daylong sit-in, demanding gender neutral family laws.
"Our protest on this special day is basically against alienating children from their parent(s) due to discriminating family laws," rights activists Jyoti Tiwari told IANS.
She said the prevailing laws are unconstitutional, and are not only against Indian social and cultural values but also violate basic human rights, and these should be amended.
Tiwari said the activists would take signatures of more than 1,000 fathers deprived of child's custody due to gender bias in laws and be meeting Prime Minister Narendra Modi shortly.
CRISP, whose activists from its regional chapters in Chandigarh, Shimla, Delhi and Lucknow participated in Sunday's protest in Delhi, demanded shared parenting and joint custody of children in divorce or separation cases.
"Our demand, on behalf of children, is basically pro-family reforms. They are voiceless victims and their rights are directly connected with both biological parents," Child Rights Initiative for Shared Parenting (CRISP) national president Kumar V. Jahgirdar said.
Quoting figures of the National Crime Record Bureau, he said 63,343 married men and 31,921 married women committed suicide in the country in 2012.
"The rate of married men's suicide incidents is almost double than of the women. In most of the separation cases, the men often either pay huge amounts of 'settlement money' to their estranged wives or commit suicide," Jahgirdar said.
To make the family laws gender specific, Save Indian Family Foundation (SIFF) president Rajesh Vakharia, said all child custody cases should be completed within six months and parental alienation should be declared as child abuse.
He said in most of the divorce cases, the men were falsely implicated in dowry and harassment cases and even denied permission to meet their children.
Another men's rights activist, Shah Ali said in the developed countries like the US shared parenting is mandatory.
"India should follow the UN Convention on the Rights of the Child as India is also a signatory. It recognises both natural parents as equal," he said.
Manpreet Bhandari, a software engineer in Bangalore who is fighting separation case, said: "The Father's Day has no relevance for people like me. Despite a court's order, I am not allowed to meet my child."