The warring rivals dug in their heels, with the Congress insisting on an apology, or at least a clarification from Modi, and the BJP rejecting the demand outright, asserting he did no wrong.
Sources in the Congress said it is likely to stall Parliament proceedings tomorrow to press for an apology from the prime minister.
The Congress today created uproar in both Houses of Parliament and disrupted proceedings. While the day's work in the Rajya Sabha was washed out, Congress members boycotted the Lok Sabha's post-lunch sitting.
Rajya Sabha Chairman M Venkaiah Naidu prodded them to sit together and find a solution across the table. Congress leaders including Ghulam Nabi Azad and Anand Sharma met Finance Minister Arun Jaitley to thrash out a solution but confabulations were of little help as none was ready for a climb down.
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Though the opposition rallied behind the Congress in the Rajya Sabha on the issue, it was isolated in the Lok Sabha with no other party joining it in boycotting the proceedings.
"The ball is in the prime minister's court," said Anand Sharma, deputy leader of the Congress in the Rajya Sabha.
The BJP, however, stuck to its guns with its spokesman Sambit Patra saying Modi had not uttered a single word for which he should apologise.
He accused the Congress of giving vent to it frustration over its defeat in the recent Assembly polls by stalling Parliament.
Patra told reporters that the Congress should instead come clean on the dinner meeting Manmohan Singh had with Pakistanis as Sharma had initially denied it took place before accepting it had.
"Our prime minister has not uttered a single word or done any wrong for which he should apologise," he said.
Even Naidu told the Rajya Sabha there was no question of an apology by anyone as nothing had been stated inside the House. He said there was no precedent of tendering apology in Parliament for statements made outside.
The Congress, in snide remarks against Modi, said he violated the Constitution and the dignity of his office by not acting against those behind "conspiracy with Pakistan", a charge he made against Manmohan Singh during the Gujarat poll campaign.
"The prime minister is trying to break the country and tarnish the image of good peple," senior Congress leader Mallikarjun Kharge told reporters outside Parliament.
Kharge said if the prime minister had information about the "secret" meeting Congress leaders, including Singh, had with the Pakistan High Commissioner and that country's former foreign minister which was "anti-national", why did he not act against them.
"If you had proof, you should have lodged an FIR against former prime minister Manmohan Singh and arrested him. You are tarnishing his image and questioning his nationalism," he said.
Azad said if Modi had a problem about tendering an apology, he should say it was a ploy to win the Gujarat election. "We will accept it," he said.
He also said had Atal Bihari Vajpayee been the prime minister "he would have apologised 10 times. It depends on who is the prime minister".