The Muslim Women (Protection of Rights on Marriage) Bill gives power to the victim to approach a magistrate seeking "subsistence allowance" for herself and minor children.
MPs from the RJD, AIMIM, BJD, AIADMK and All India Muslim League opposed the bill, calling it arbitrary in nature and a faulty proposal.
Prime Minister Narendra Modi earlier called for consensus in passing the bill.
He also said a message has gone down as to who was playing "vote bank politics".
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He also said the Congress also stands exposed by not opposing the bill.
CPI(M) leader Brinda Karat criticised the government for attempting to push the bill through Parliament without holding any discussions or consultations with Muslim women and women's organisations.
"This bill is a historic step towards ensuring dignity for Muslim women. I thank all fellow Parliamentarians who have supported this bill, which will bring a new era of hope and respect in the lives of Muslim women," BJP chief Amit Shah tweeted.
Speaking to reporters outside Parliament, Law Minister Ravi Shankar Prasad said the bill is not about any religion but about the issue of women justice and dignity.
His colleague Mahesh Sharma said it is a bill that respects humanity and helps provide dignity to our mothers and sisters.
Supporting the bill, the Congress said Parliament must ensure the protection of rights of Muslim women and children under all circumstances.
Congress's communications department in-charge Randeep Surjewala said it was the first political party to welcome the Supreme Court verdict banning triple talaq, and had hailed it as a decisive step towards women empowerment and victory for the rights of Muslim women.
"The present bill needs to be strengthened to safeguard the rights of women to a life of dignity with adequate subsistence allowance. Parliament must ensure protection of rights of Muslim women and children under all circumstances," he said.
However, senior Congress leader Salman Khurshid, a former union law minister, struck a discordant note, insisting the proposed law will be an "intrusion" into the personal lives of individuals and bring divorce, a civil issue, into the realm of criminal law.
"Criminal law is kept out of family as far as possible, which is a general policy everywhere. Why are we bringing criminal law into something which is a non-existing factor? Triple talaq is no institution or institutional fact of life, the Supreme Court has made it very clear," Khurshid said.
CPI(M) leader Karat said the bill "itself is very objectionable, and equally objectionable are the efforts of BJP to push it through Parliament without any consultation or discussion with those in whose names the bill is been passed".
BJP Spokesperson GVL Narasimha Rao tweeted, "To Appeasers' Alliance comprising Owaisi, RahulG, Mamata; Mulayam, Lalu: Stop communal politics! Jail provision of up to 3 years for Instant Triple Talaq is reasonable. Hindu Marriage Act has stronger provisions: for 2nd marriage jail term is up to 7 years under IPC Section 494."
BJP's youth wing president and party MP Poonam Mahajan said, "For so many years, politics took precedence over women's rights. A historical step is taken today in Parliament for empowerment of women with the passing of the Triple Talaq Bill. I thank Narendra Modi and Ravi Shankar Prasad for this significant decision."
He said the bill should ensure payment of maintenance and/or subsistence allowance to women and children if the husband is in jail for 3 years, as envisaged under the law.
Terming the bill as "very important" and "significant", Mahila Congress chief and party spokesperson Sushmita Dev said her party will work with the government to bolster the rights of Muslim women.
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