The Income Tax Department has also initiated a probe into the mining contracts.
An official statement said Rana has offered to resign in order to ensure a free and fair investigation into the matter, however the chief minister asked him to continue till the outcome of the judicial probe.
A one man judicial commission has been set up to probe the allegations of impropriety against the state irrigation and power minister in the multi-crore sand mining auctions held recently by the state government, an official spokesman said.
The terms of reference for the inquiry commission, formed under the Commission of Inquiry Act, would be notified soon, the release said.
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Amarinder announced his decision to set up the commission after taking suo motu cognisance of media reports accusing the minister of acquiring certain mines in the names of his company's staff, it said.
Rana has denied any links of his company, Rana Sugars Limited, with the auctions and has said his company has no stake, direct or indirect, in the sand mining business.
Opposition parties, the AAP, the SAD and the BJP, have been demanding immediate sacking of Rana for allegedly acquiring sand and gravel mines through "benaami transactions in the name of his former cook and staff".
The political parties have also been questioning the "silence" of Amarinder on the matter. They have dared him to remove Rana, describing it as the his "biggest test" as the chief minister has been claiming that his government was tough against corrupt practices.
Another 56 mines would be put to auction on June 11 and the government is expecting to generate another Rs 300 crore from them. The state government's revenue from the mine auction last year was merely Rs 40 crore.
The opposition had also raised questions over the allotment of mining contracts to Amit Bahadur at Saidpur Khurd village in Shaheed Bhagat Singh Nagar for Rs 26.51 crore, Kulvinder Paul Singh at Mehadipur in SBS Nagar for Rs 9.21 crore, Gurinder Singh at Rampur Kalan village in Mohali district for Rs 4.11 crore and Balraj Singh at Bairsal village for Rs 10.58 crore.