Congress Vice-President Rahul Gandhi, Sonia Gandhi's daughter Priyanka Gandhi and son-in-law Robert Vadra also endorsed it by signing the campaign.
Rajiv Gandhi, who served as the sixth Prime Minister, was assassinated in a suicide bombing at Sriperumbudur in Tamil Nadu on May 21, 1991.
"Remembering my father today".
"We want to realise Rajiv ji's dream of empowering women, and will carry out a door-to-door campaign collecting signatures", said Mahila Congress president Shobha Oza. A leader driven by love, compassion and a deep generosity of heart.
Describing Rajiv as a "messenger of peace", Chidambaram said the former prime minister had initiated various peace agreements in Punjab, Mizoram, Kashmir and Assam during his tenure. It aims to ensure 33 per cent seats for women in state Assemblies and Parliament.More news: Drake wins record 13 Billboard Music awards
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NCP leader and former Congressman Sharad Pawar tweeted an old photo of him with the late prime minister. The Mahila Congress had zeroed in on the assassination day of Rajiv Gandhi (May 21) to launch the campaign.
The nation-wide campaign, which will last till August 20, Gandhi's birth anniversary, will pressurise the NDA government to pass the Bill.
Rajiv Gandhi had succeeded his mother Indira Gandhi after her assassination in October 1984.
The Indian Youth Congress had organised another programme in the evening to mark the occasion, but had to cancel it due to heavy rains.