"The Indian government appointed an arbitrator but he resigned in May 2015. The third arbitrator, who will act as chairman of the tribunal, had been agreed by the two party-appointed arbitrators (prior to the government's arbitrator's resignation) but declined to accept the appointment.
"There is now likely to be a delay in appointing the chairman pending the Indian government appointing a replacement for its party-appointed arbitrator," Vodafone said in a statement.
Vodafone nominee Yves Fortier of Canada, however, continues to be on the panel.
The British telecom giant further said that if there is no subsequent agreement on appointment of the chairman, the International Court of Justice will appoint the third arbitrator.
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The dispute is over tax liability arising out of Vodafone's 2007 purchase of Hutchison Whampoa Ltd's Indian assets.
Following an international arbitration notice by Vodafone, the previous UPA government in May 2014 had approved the withdrawal of a conciliation offer.
While the basic tax demand was Rs 7,990 crore, the total outstanding, including interest and penalty, is estimated to have risen to Rs 20,000 crore.
The Supreme Court had ruled in Vodafone's favour in 2012, saying the company was not liable to pay any tax over the acquisition of assets in India from Hong Kong-based Hutchison.
The government, however, amended the tax laws with retrospective effect to undo the Supreme Court judgement and claim taxes.