The AAP demanded sacking of the state irrigation and power minister while the SAD and the BJP demanded a probe into the matter.
However, Rana Gurjit denied the charges saying neither he nor his company - Rana Sugars Limited - has any direct or indirect stakes in sand mining business.
A week ago, a two-day e-auction of sand mines in Punjab culminated with bids worth Rs 1,026 crore secured for 89 mines, the highest ever earnings for the state from sand mining sector.
Senior SAD leader Prem Singh Chandumajra said the minister, who had allegedly openly abused his authority to indulge in "naked illegality", should be prosecuted under relevant sections of the Income Tax Act.
"The case should also be handed over to the Enforcement Directorate for probe as someone who was making 'paranthas' till last night has outbid 32 other bigwigs to acquire a Rs 26.51 crore mining site," the SAD lawmaker alleged in a statement.
Informing that his party would raise the issue in parliament, he said the state government should answer why it was "letting cooks and employees of Rana Gurjit, who were paid a couple of thousand as salary, to participate and win auctions by submitting bids of Rs 50 crore".
Citing media reports, Tarun Chugh, the national secretary of the BJP said, "Rana Gurjit Singh's cook and other employees getting mining contracts worth crores is a classic example of what the Congressmen are up to."
"His cook Amit Bahadur got sand mines worth Rs 26.51 crore in Saidpur Khurd of Nawanshahr. It is surprising as to how a person, cooking meals in Rana's Sugar Mill could participate in an auction and strike a deal worth over Rs 26 crore," he said.
However, Rana Gurjit claimed that neither his family members nor employees have any links with sand mining business and termed as "incorrect" the reports in a section of the media which claimed that two of his company employees had successfully bid for sand mines. He said the employees in question had left their jobs a long time ago, which can be verified from the company's records.
"Though I am personally not involved in the day-to-day functioning of my companies for the last two decades, I can say with command and confidence that neither any person working in these companies nor any of my family members has any interest or stake in sand mining business in Punjab," the minister said.
"Amarinder is keeping his eyes closed. He should explain his silence that what is stopping him from taking action against Rana Gurjeet Singh?" he said.
Meanwhile, H C Arora, local lawyer, wrote to the Enforcement Directorate seeking investigation into the matter.