The bill, which has divided political parties and drawn criticism from several Muslim bodies, was passed by the Lok Sabha on December 28. It now has to be passed by the Rajya Sabha to become a law.
But the Congress, which supported the bill in the Lok Sabha, wants certain changes to the bill - such as making provisions for providing financial aid to Muslim women divorced through instant triple talaq - before supporting its passage in the upper House.
Congress leader Pramod Tiwari said even parties like the TDP and the BJD, which have stood with the BJP, were with the opposition on the issue. Even "independent" parties like the INLD have distanced themselves from the BJP, he added.
"The BJP has neither the policy nor the intention to get the triple talaq bill passed in Parliament," he told reporters.
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Tiwari alleged that it was the BJP's policy to "divide the society" and the ruling party was running away from a debate on the matter.
On the Dalit protests in Maharashtra, Tiwari alleged that wherever the BJP has been voted to power violence against the community has increased.
"Whenever BJP is in power or is seeking to gain power, its first attack is on breaking the society on caste and religious lines," he said, adding that it's attempt in Maharashtra was also to creak social harmony in the society.
Senior Congress leader P L Punia alleged it was clear that the BJP and the RSS ignited violence in Koregaon village in Pune district on January 1 and the Maharashtra government failed to control the violence there.
Punia alleged that the two accused, who were linked to Hindutva outfits, were stated to be close to Prime Minister Narendra Modi and Maharashtra CM Devendra Fadnavis.
"We demand legal action against those who were trying to disturb harmony (in the society)," he said.
He claimed that the Pune violence was spreading to other states like Gujarat and Madhya Pradesh.
"The BJP and RSS does the work of dividing society on caste and religious lines. Dalit atrocities also rise wherever the BJP is in power," he alleged.
"AADHAR data breached yet again! As every citizen's personal information is exposed to hackers everyday & Right to Privacy is mocked and flouted with impunity, Modi Govt remains immune. Is anyone listening?," Congress communications in-charge Randeep Surjewala tweeted.