Describing the judicial inquiry initiated into the allegations as "farce, pre-determined and a mere eye wash", the party alleged that the Congress government in the state is "hell-bent" upon saving the tainted minister.
AAP state co-president Aman Arora alleged, "Involvement of cabinet minister Rana Gurjit Singh in the recent e-auction of sand mines has been exposed."
"Instead of taking any action against Rana Gurjit, the government is hell-bent upon saving him by appointing a single-judge commission to inquire the matter. The panel member's proximity to the minister's family is well known," the MLA from Sunam said.
Arora said the AAP and the Lok Insaaf Party will take the "matter of corruption by the minister" to the streets if no action is taken by the state government.
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He said the AAP will start demonstrations in the coming days at various place in Punjab.
Sukhpal Khaira, the party's chief whip and Sarabjit Kaur Manuke, its deputy Leader in Punjab Assembly will lead the protest in Jalandhar on Monday while Sadhu Singh will lead protests at Faridkot on June 8, Arora said.
The opposition parties have accused the state irrigation and power minister of acquiring sand and gravel mines through benaami transactions in the name of his company's cook and staff, a charge denied by him.
A two-day e-auction of sand mines in Punjab held last month culminated with bids worth Rs 1,026 crore secured for 89 mines, the highest ever earnings for the state from sand mining sector.