Reliance and Royal Dutch Shell own 30 percent interest each in the fields on west coast, while Oil and Natural Gas Corp holds the remaining 40 percent.
Government sought $3 billion from the companies after an international tribunal upheld the government's view that profit from the fields be taxed at the current rate of 33 percent and not the earlier 50 percent, the Economic Times newspaper reported on Tuesday.
Shares of Reliance fell 2.05 percent on Tuesday to Rs 1,519, dragging the BSE Sensex lower.
The government has sought the additional payments in line with the arbitration tribunal's final partial award dated Oct. 12, Reliance said.
"The quantification of liabilities (if any) of the parties arising out of the Partial Award have to be determined by the Arbitration Tribunal after the Parties have made their respective submissions on quantification," the company added.
The arbitration tribunal is yet to schedule the timeline for the quantification phase, Reliance said, adding the company had already responded to the government's demand notice.