NEW DELHI—India’s federal cabinet on Wednesday approved two deals worth about $3 billion that will allow a consortium of Indian state-run oil companies to buy stakes in two Russian oil fields, a top government official said.

A consortium of Oil India Ltd., Indian Oil Corp. Ltd. and Bharat Petro Resources Ltd., which is the exploration and production arm of Bharat Petroleum Corporation Ltd., had in March agreed with Russian state-run oil company Rosneft to buy a 23.9% stake in its Vankor oil fields. The deal, worth about $2.02...