McHugh, who had previously declined to become an arbitrator in the dispute but later relented and accepted the offer, formally sent an email withdrawing from the case, sources said.
The apex court had on April 29 named McHugh, former judge of the High Court of Australia, as the third arbitrator in the dispute over cost recovery in KG-D6 gas block.
In November 2011, RIL had started arbitration proceedings against the government, seeking a decision on its entitlement to recover investments made in the KG-D6 gas field from sales.
The cost disallowed was raised to USD 2.376 billion for output lagging targets in four years ending March 31, 2014.
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RIL and its partners say the action is not as per the Production Sharing Contract (PSC) and they are entitled to recover all costs of the block in the Bay of Bengal.
However, the arbitration couldn't start as the government refused to play ball and it was only after two-and-a-half years that the third arbitrator was appointed by the Supreme Court.