While the two refused to comment on discussions they had with Sitharaman, Mittal said the telecom sector has been under stress for the last three-and-a-half years and the government should focus on its sustainability.
Mittal, who heads mobile service major Bharti Airtel, first met Telecom Secretary Anshu Prakash before going for the meeting with the finance minister.
Birla, who is the chairman of Vodafone Idea Ltd, had met the telecom secretary on Tuesday.
It was not immediately clear if the two telecom tycoons met Sitharaman together or separately.
Emerging out of the North Block after meeting Sitharaman, Mittal told reporters that the issue of pending dues arising out of the Supreme Court ruling on Adjusted Gross Revenue (AGR) was not discussed.
The telecom industry, he said, is vital to India's digital agenda.
"This industry is very vital to the nation's digital agenda, and many other industries that ride on it....employment, government taxes...the only thing government needs to focus on is how to ensure sustainiability of the sector," Mittal said.
Mittal -- whose company Bharti Airtel is confronted with over Rs 35,000 crore of statutory dues -- did not elaborate on the relief mechanism that the telco is pitching for. The industry as such has been batting for reduction in levies like licence fee and spectrum charges.
Mittal said Airtel has already announced its plans to pay the dues that arose from the apex court ruling. The company is calculating its liability, he added.
Airtel has so far paid Rs 10,000 crore out of its estimated liability of over Rs 35,000 crore.
"We have made statement that we are working on the calculation so as soon as it is ready...," he said.
Vodafone Idea Chairman Kumar Mangalam Birla refused to comment on whether the company has approached the government for relief on the timelines for the statutory payment, and whether he has received any assurances in return.
Asked about the mounting stress in the telecom sector, Birla said, "That is in the public domain...there is no other insight I can add."
On whether it is a do-or-die moment for telecom companies like Vodafone Idea, Birla said, "Let us see."
Vodafone Idea on Monday paid Rs 2,500 crore to the Department of Telecommunications (DoT) and promised to pay another Rs 1,000 crore before the end of the week.
But the amount paid for now is less than 5 per cent of the dues that the DoT estimates the company owes to the government following the Supreme Court ruling that asked for including non-core revenues of telcos in computing statutory payments such as licence fee and spectrum charges.
The Supreme Court on Monday refused to stop the telecom department from taking any coercive steps for recovery of dues from Vodafone Idea.
In December, Birla had said Vodafone Idea may have to shut down if there is no relief on statutory dues. "If we are not getting anything, then I think it is the end of the story for Vodafone Idea," Birla had said. "It does not make sense to put good money after bad... We will shut shop."
After a Supreme Court rap on February 14 for missing the payment deadline, top telecom firms Bharti Airtel, Vodafone Idea and Tata Teleservices earlier this week scrambled to pay a part of their outstanding dues.
Airtel -- which recently raised USD 3 billion -- has paid Rs 10,000 crore to the government, and said it will clear the remaining dues before the next date of hearing on March 17. Vodafone Idea, however, has so far not provided a clear deadline for making balance payments.
Tata Teleservices paid Rs 2,197 crore, the entire outstanding it believes to have arisen after the October ruling of the apex court for calculating dues after adding non-telecom revenues. It has also submitted to DoT the details of calculations in support of the payment.
The DoT -- which last week drew flak for ordering no coercive action even after telcos missed the January 23 payment deadline set by the Supreme Court -- had been mulling the option of encashing bank guarantees given by firms when they got telecom licences, as none of the telcos paid the full amount. The telecom department would seek opinion from the law ministry on the issue, sources said.
The Supreme Court, last week, rejected a plea by companies such as Bharti Airtel and Vodafone Idea for extension in the payment schedule and asked all of them to deposit an estimated Rs 1.47 lakh crore in past dues for spectrum and licences. It threatened to initiate contempt proceedings against top executives of these firms for non-payment.
Some telecom firms are already struggling with mounting losses and debt and the additional liability has raised concerns of them defaulting on existing loans. Of the estimated dues that include interest and penalty for late payments, Airtel and Vodafone Idea owe about 60 per cent. MBI DP ANZ ABM