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 government had disallowed as much as USD 1.005 billion of its investment as KG-D6 output lagged targets. Production from main fields in the block was way short of 80 million standard cubic meters per day target.
The cost disallowed was raised to USD 2.376 billion for output lagging targets in four years ending March 31, 2014.
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.
Withdrawing from the Tribunal, McHugh had stated that would not be available before September 15 due to his previous preoccupations and since the Supreme Court wanted the process to be expedited, he would not be able to act as the Chairman of the tribunal.