While the government wanted a debate on the Muslim Women (Protection of Rights on Marriage) Bill in the Rajya Sabha, the opposition wanted it to be sent to a Select Committee for scrutiny before it is a made a law.
The Lok Sabha has passed the Bill last week.
The BJP accused the Congress and other parties of running away from a debate and stalling the bill that ensures gender justice to Muslim women.
With only two days left for the winter session to end and with both sides adamant on their stand, the passage of the bill appears uncertain.
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Asked about the fate of the bill, Finance Minister Arun Jaitley said, "We will see tomorrow when it comes before Parliament."
Leader of the Opposition in the Rajya Sabha Ghulam Nabi Azad said the opposition wanted the bill to be sent to a Select Committee that would help make it strong by offering support to Muslim women and by removing the criminality clause.
He, however, exuded confidence that the Congress and other opposition parties would have to support the bill considering public opinion in the country.
"It has become clear that the Congress party is indirectly opposing the triple talaq bill. It was a mere sham that they gave a statement and supported the bill. They tried their best to ensure that this bill is not passed in the Rajya Sabha," Jaitley told reporters outside Parliament.
Azad, on his part, said it is Parliament which decides on the floor if a bill will go to a select committee or not.
He accused the BJP of "befooling" Muslim women with the triple talaq bill that seeks to make the practice a criminal offence, alleging that it has no provision for their welfare in case their husbands are jailed.
Azad said 18 opposition parties, including the Congress, wanted the bill to be sent to a Select Committee for its proper scrutiny before it becomes a law but the government did not allow.
"This government is trying to mislead Muslim women and the general public," he alleged at a press conference.
"What are they giving to Muslim women. They are merely projecting themselves as their 'messiah', but they are in fact only trying to befool the Muslim women," he said.
Congress leader M Veerappa Moily opposed the provision of criminalising triple talaq, alleging the BJP adopted "sadistic approach" and was "taking revenge" against a community.
Trinamool Congress leader Derek O'Brien said the BJP did not want the bill to be passed in the Rajya Sabha and its "double standards" were exposed when it "disrupted".
"What happened in the Rajya Sabha was historic. The government created disruptions in the Rajya Sabha. They are not interested in passing the bill. The BJP is playing dirty politics over women, over religion. This is the only way to expose the double standards of the BJP," he said.
In the Upper House, opposition parties such as the Congress, TMC, CPI(M), CPI, SP, BSP, DMK, AIADMK and BJD, along with the BJP's ally TDP, today moved a motion asking the bill to be sent to a select committee.