The move came in the wake of government's refusal to settle the dispute through arbitration over recovery of cost incurred by the company in developing the D6 hydrocarbon field in the KG Basin.
The petition filed by RIL said it has already appointed former Chief Justice of India S P Bharucha as arbitrator but the government has not done so as per the contractual obligation.
In the petition, RIL has asked the Chief Justice of India S H Kapadia to appoint a second arbitrator on behalf of the government.
The petition filed through advocate Sameer Parekh said that as per the contract government cannot reduce the recovery amount.
The petroleum ministry had proposed to restrict the cost of around Rs 6,343 crore which the company had sought to recover for developing the KG D6 field.
RIL had issued an arbitration notice to the government on November 23, 2011, proposing appointment of a former chief justice of India S P Bharucha as arbitrator in the dispute and asked the ministry to appoint a second arbitrator.
However, the government has refused the plea of RIL saying there is no dispute, the advocate said.