General Singh had clarified that his statement had been "distorted" and he didn't intend to hurt any section of society.
Prime Minister Narendra Modi has planned a number of ways to pay homage to Baba Saheb Ambedkar this year, but the Opposition says remembering the man who empowered India's oppressed classes will be meaningful only if PM Modi takes action against his minister, General VK Singh.
"He (General Singh) has made a statement that's' insulting and insensitive, particularly against Dalits, clarification does not matter...it for the Prime Minister to decide whether he is an asset or a liability," said Anand Sharma, Congress' deputy leader in Rajya Sabha.
On October 22, General Singh was asked to comment on the incident in which two Dalit children were burnt alive in Haryana -- a BJP-ruled state. But the minister's reported response -- "If someone throws stones at some dogs, will the Prime Minister be held accountable" -- had created a huge controversy.
General Singh had clarified that his statement had been "distorted" and he didn't intend to hurt any section of society. The Opposition, however, has not accepted his clarification.
Last week, the Rajya Sabha was repeatedly adjourned after the Bahujan Samaj Party and the Congress objected to General Singh's presence in the House.
The government has strongly defended the minister, arguing as an elected member, he was entitled to sit in Rajya Sabha.
The Opposition is further enraged after the minister wrote about his Rajya Sabha experience in a Facebook post. "We will move a notice of breach of Parliamentary privilege for hurting the sentiments of the Upper House," said KC Tyagi of the Janata Dal United.
The government accuses the Opposition of politicising the issue. "He has clarified, once, twice, thrice...even ten times. After this the issue should be closed, but if someone wants to play politics that's a different matter," said Union minister Mukhtar Abbas Naqvi.
Keen to pass crucial legislations, including the flagship Goods and Services Tax or the GST bill, the government wants to avoid confrontation. But as the Winter Session enters a new week, the Opposition and the government could be headed for a fresh round of face-off.