Puri was speaking at a meeting with Air India's employees' unions here on Thursday.
The Indian Commercial Pilots' Association (ICPA), one of the unions which was present in the meeting, said that all the unions opposed privatisation, but the minister stated that the government does not have funds to infuse into Air India.
"The meeting was called to have constructive dialogue and address the genuine concerns of the employees," the ICPA said in a statement late on Thursday evening.
Puri, the union said, said that Air India will run till its privatisation and requested all the unions to cooperate towards the process.
According to the ICPA, the minister expressed his displeasure over pilots and engineers demanding the government-owned airline to waive off their notice period.
He said pilots and engineers are required to run the airline, the union added.
Last week, the ICPA in a letter to Puri said: "It is unfair for the Government of India to keep us bonded with the notice period while we are not being paid on time and our dues are not cleared."
Terming the Civil Aviation Minister's earlier statement that if Air India is not privatised by March 31, 2020, the airline will be shut down as "a matter of concern", the pilots' union had said in the letter: "With this uncertainty over the survival of our national carrier and with no 'Plan B', we request you to ensure that we are not treated like bonded labour and allow us to quit Air India without serving the notice period and clear all our dues immediately."
At present, the union has 800 pilots as its members. As per the letter, currently 65 pilots have tendered their resignations and are serving the six-month notice period which is due for completion "very soon".
The Centre is likely to issue the expression of interest (EoI) for divestment of its stake in the national passenger carrier during the first month of 2020.
Union Home Minister Amit Shah heads the panel looking after the divestment process. Its other members include Finance Minister Nirmala Sitharaman, Commerce and Railway Minister Piyush Goyal and the Civil Aviation Minister.
In the previous Modi government, then Finance Minister Arun Jaitley headed the ministerial panel called the Air India Specific Alternative Mechanism (AISAM).
After failing to find a bidder then, the government is working on a war footing to sell Air India to a private player.
( With inputs from IANS )