The government has made it clear that there will be no apology or explanation, with Mr Jaitley accusing the Congress of a "complete misadventure." But at the suggestion of Vice-President M Venkaiah Naidu, who is also the chairman of the Rajya Sabha, that an amicable solution be found, the opposition and the ruling party decided to form a committee to do that.
This morning, as parliament convened for the third day of a curtailed winter session, Congress members again protested over the PM's remark, stalling proceedings in both Houses for short periods.
The opposition created a ruckus in the Rajya Sabha the moment Question Hour began at noon. It continued till Mr Jaitley got up to assure opposition leaders about the government's willingness to address their concerns. An hour later, the Congress walked out of the Lok Sabha after the Speaker repeatedly refused to allow them to raise the issue.
In the Rajya Sabha, Mr Naidu said he had met senior leaders from both sides to try and address the problem. He said he also met Dr Singh, who has denied the allegations in a strong statement last week that ripped into the BJP and the government, accusing them of spreading "falsehood and canards to score political points."
"All things can be internally discussed and seen that the House functions properly and dignity of Parliament should be maintained," Mr Naidu said.
Mr Jaitley, who is Leader of the House, offered to talk to Ghulam Nabi Azad, who is Leader of the Opposition in the Rajya Sabha.
"We will try and explore a solution out of that...We will try and do it today," Mr Jaitley said, suggesting setting up a committee.
Both Houses have been functioning since and the Rajya Sabha also passed a bill on management institutes that had been pending for months.
But with both sides unwilling to back down for now, it is still unclear what could be a meeting ground.
Congress leader Anand Sharma later told reporters that the party had given its proposal to the government and was yet to receive a response.
Congress leader Mallikarjun Kharge, who led his party's MPs in the walkout of the Lok Sabha, later told reporters outside Parliament, "Prime Minister Modi ji made allegation in Gujarat election without verifying facts purposely; he defamed our former PM along with his 16-17 members. Also former army chief, former commissioner, who served the country. We want to know from Prime Minister Modi what are the mistakes they have done. Have they really conspired against Modi ji during election?"
The Congress has asked why PM Modi chose to make his allegation at an election rally rather than use intelligence and investigation agencies to find out if the charges against Dr Singh are true.
Parliamentary Affairs Minister Ananth Kumar has slammed the Congress, saying the party's conduct today in the Lok Sabha was "shameful and condemnable".
In results announced yesterday, the BJP has retained Gujarat, but by a lower margin of victory. The BJP has attributed its narrower win in PM Modi's home state to what party chief Amit Shah has called the Congress' "caste politics and low political discourse.
PM Modi was addressing an election rally in Gujarat before it voted in the final phase, when he accused Pakistan of trying to meddle in the Gujarat elections, also saying that Congress leaders including Dr Singh discussed the Gujarat polls at a dinner hosted by suspended Congress leader Mani Shankar Aiyar.
The winter session of parliament, which is usually held from the middle of November, began last Friday, December 15, and has just 14 working days. The government has listed at least 25 pending bills and bring in 14 new bills in the session including the much-talked about bill to ban instant Triple Talaq. Three ordinances issued in recent months will also come up for a vote.