"Today (Tuesday) is the cut-off point," Argentine Labour Minister Patricia said after meeting members of the technicians union (APTA) and the flight attendants' union and the controlling shareholder, the Spanish state holding company, SEPI.
"If there is no agreement... we will be in a very precarious situation because there is no more money to finance the business," she said.
SEPI has reportedly warned it could close Aerolineas Argentinas by Friday if the airline's seven unions don't sign an agreement on new work rules, lower salaries and a schedule for layoffs.
Two of the seven unions have rejected the offer and demanded the salaries of 7,000 workers which SEPI withheld in April be paid.
Ms Bullrich said after the meeting that she would filed a suit immediately in Argentine courts to have the technical union's legal status as a bargaining unit removed.
Workers protest
Meanwhile in Buenos Aires, some 120 Aerolineas workers threatened to block departing flights of Spain's Iberia in protest over the unpaid wages.
"If Aerolineas doesn't fly, neither will Iberia," Ariel Basteiro, head of the Airline Personnel Association, told the local media.
Workers and the Argentine government are increasingly worried that the half-century-old flagship airline, a national symbol, will shut down.
Thousands could lose their jobs at a time when Argentina is in a 3-year-old recession and battling 15% unemployment.
Officials from both governments have said that they will not use public money to bail out the troubled flagship carrier, saying the problem is "business, not political".
A nine-day strike that ended 2 May touched off the airline's latest labour and financial problems after the unions protested plans to lay off more than 500 workers.
Spain's offer
SEPI is reported to be preparing to sell its 93% stake in the airline, which has debts of $900m, but plans to inject $350m to keep it afloat provided there is industrial peace.
A deal would involve job stability for two years in exchange for the unions accepting more flexible contracts, wage cuts of between 6% and 20%, and extensive job losses.
The airline is currently losing about $20 to $30m a month.
"Without this capital injection, Argentina is not in a position to take on the company, and it would be headed down a very painful road of either starving to death or going broke," Ms Bullrich said.
Five of Aerolineas Argentina's seven unions have accepted the SEPI plan but the technicians and flights attendants union have rejected it fearing massive job losses and wage cuts.
The Argentine government still owns a 5.4% stake in the airline, which was debt-free at the time of its privatisation in 1990.