"If we are not getting anything then I think it is end of story for Vodafone Idea," Birla said at a leadership summit organized by a local daily. "If you ask me specifically, it is true that we will shut shop if we don't get relief."
Birla was responding to a question about the company's course of action in moving forward in the absence of government relief.
He said Aditya Birla Group, the parent company, will not invest any money in Vodafone Idea in the absence of relief from the government.
"There is no sense that good money should follow bad money," he said.
Vodafone Idea is the third-largest mobile service provider in India.
Birla's Idea Cellular and British telecom giant Vodafone's India unit merged last year to carry out business in India.
It posted the biggest quarterly loss after it provisioned for the payment to the department of telecommunications, following the Supreme Court upholding the government's position in the adjusted gross revenue (AGR) matter.
Vodafone and another telecom company have petitioned the government for relief in waiver of interest and penalty in payment of telecom license fee and spectrum usage charges.