An angry opposition led by the Congress accused Modi of levelling "serious charges" against Singh, former Vice President Hamid Ansari and diplomats.
Chairman M Venkaiah Naidu disallowed a notice by Congress and other opposition members under rule 267 for suspension of the business of the House to discuss the matter, which led to further noisy scenes.
The Upper House saw three adjournments before the Chair finally called it a day, a little after 3 PM following continued uproar and slogan-shouting.
They raised the issue soon after the Chairman informed the House about his decision to disqualify the two former JD(U) members after giving them due opportunity of hearing.
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As the members protested, Naidu said there cannot be any discussion on the decision of the Chair. "There is no discussion on the ruling of the chairman. Please sit down."
"This is a political issue which you are raising, which you discuss outside the House. I have no problem," he said, adding "this is not the manner.... All are standing...Both the sides are standing.. I have not allowed."
When the House reassembled at noon for Question Hour, Leader of Opposition Ghulam Nabi Azad raised the issue of Modi's remarks at an election rally in Gujarat targeting Singh over a dinner meeting with Pakistani diplomats.
Azad said his party and other opposition leaders have given a notice under rule 267 seeking suspension of the listed business to discuss an issue which he termed as "serious".
"There are charges ... many foreign secretaries, high commissioners and ambassadors... charges have been levelled on them that they are hatching a conspiracy with Pakistan in Gujarat election. The PM on December 10 in Palampur in Gujarat has levelled this allegation. This is not an ordinary allegation...against a former PM, vice president and Army chief," Azad said.
But Naidu disallowed it, saying "I have gone into the notice given by Ghulam Nabiji, Naresh Agarwal...I have not allowed it ...pls sit down."
When the House met again, Azad raised the issue amid the uproar and the House was adjourned again till 3 PM by deputy chairman P J Kurien.
While Kurien pleaded with members to take up the private members' business, Samajwadi Party member Naresh Agarwal raised the issue of the Centre's move to set up special courts for cases against MPs and MLAs and questioned the move.
When Kurien said it was a decision of the Supreme Court, Agarwal said he had not criticised the top court but his questions were directed at the government.
Minister of State for Parliamentary Affairs Vijay Goel asked how the issue being raised was a point or order, which, he said, was related to the business of the House.
Meanwhile, several Congress members were on their feet by this time and started raising slogans demanding an apology from the prime minister for his remarks.
Several Congress members including Oscar Fernandes, Shamsher Singh Dullo, Renuka Chowdhury, Sanjay Singh trooped into the Well of the House shouting slogans.
As the slogan shouting continued, Kurien adjourned the proceedings till 3 pm. When the House reassembled, opposition members continued their protests, forcing Kurien to adjourn the House for the day.
Earlier when the House assembled, Chairman Naidu led the House in paying tributes to ten former members who passed away during the inter-session period. Thereafter, the Prime Minister introduced new ministers to the House.