While leaders of Trinamool Congress, RJD, JD(U) and AIUDF and some other parties joined the Congress-led delegation, NCP, DMK, Left parties, Samajwadi Party and Bahujan Samaj Party stayed away.
The fissures in the opposition unity cropped up at the last minute after a Congress delegation met the Prime Minister separately in Parliament House on farmers' issues and demanded loan waiver for farmers.
The delegation, led by Congress President Sonia Gandhi, party Vice President Rahul Gandhi and former Prime Minister Manmohan Singh, with a host of leaders from various opposition parties being part of it, later handed over a memorandum to the President.
"The demonetisation decision has brought about a disastrous situation in the nation. We beseech you, as the protector of the Constitution, to kindly intervene to save the people from economic disaster," the memorandum said.
Congress leader Mallikarjun Kharge said the leaders apprised the President of the situation arising out of demonetisation and the problems being faced by them.
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Kharge said the opposition leaders wanted to highlight the problems faced by people due to demonetisation.
"The government is fully responsible for not allowing Parliament to function. They have thrown all rules to the winds," he said.
Trinamool Congress leader Sudip Bandyopadhyay said the purpose of meeting the President was to apprise him that representatives of people are not being able to reflect their observations after demonetisation.
"The government has miserably failed to give proper direction on what is the way out of this situation after demonetisation. They avoided Parliament and chose to speak outside Parliament. We wanted a debate in Parliament," he said, adding that the ruling party is unable to explain why they did not allow a discussion.
Sharad Yadav said no effort was made by the government to allow the problems of people to be discussed in Parliament.
RSP leader N K Premchandran said, "Democratic Parliamentary system in India is under threat."
They opposition leaders said the demonetisation decision has a "devastating and crippling" effect on the common people of the country.
"It was our expectation that after such a draconian decision by the Prime Minister himself, he as the architect of this announcement, would personally make a suo motu statement on the first day of Parliament regarding this issue. We were shocked when no such statement was forthcoming from the Prime Minister, as it is the normal convention in Parliamentary procedure," the memorandum said.
While SP's Naresh Agrawal and NCP's Praful Patel said it would have been better had the Congress taken the entire opposition together and had it not met the Prime Minister separately on farmers' issues, CPI(M) leader Sitaram Yechury said that they will go the public instead of going to the President.
Protests over demonetisation have disrupted parliamentary proceedings during the entire winter session of Parliament, which has been a virtual washout.
