Vito Riggio, the head of Enac, said: "If there is nothing concrete on the table, in a week, or 10 days at most, the planes will no longer be able to fly. Of course, we hope that will not happen."
Alitalia said that passengers on the cancelled journeys were being put on alternative flights, but many travellers preferred to go by rail, with two extra trains being laid on between Milan and Rome.
The company insisted that ticket sales, reservations and flights were all operating normally, while the government appeared not to have given up hope of tempting the consortium, which had originally offered to save the company, back to the table.
|Alitalia employees demonstrate during a meeting with the CAI consortium [AFP]
The Italian Air Company (CAI) withdrew its $1.4bn takeover offer on Thursday after six out of the Alitalia's nine trade unions rejected a deal which would have led to 3,250 job losses.
The consortium said it had made many concessions but any more would have put the realisation of the plan at risk, especially given the current turmoil in global financial markets.
Altero Matteoli, Italy's transport minister, said: "There are still contacts, we are trying to revive negotiations with the CAI but the situation is desperate."
If the CAI withdrawal is confirmed "there is no other outcome but bankruptcy", Maurizio Sacconi, the country's labour minister, said.
Meanwhile, Augusto Fantozzi, Alitalia's government-appointed administrator, who will also meet ENAC on Monday, said: "We will do all we can to keep Alitalia alive."
But he admitted that other major foreign airlines he had contacted had shown no interest in taking on Alitalia.
A spokesman for Lufthansa declined to comment on a report in La Repubblica, the Italian newspaper, that the German airline could be a "white knight".
Only $43m to $72m of a $430m emergency loan granted by the government in April is likely to remain by the end of September.
News reports in Italy said Fantozzi could keep Alitalia flying for a few more weeks, including by selling off a number of subsidiaries and continuing to lay off workers.
The failure of the CAI bid was a blow to Silvio Berlusconi, Italy's prime minister, who had promised before elections this year that the airline would remain under Italian control.
Alitalia, which was founded in 1946, has suffered from continuous political interference in a country whose governments have been notoriously short-lived, preventing it from building a long-term strategy.
The government holds a 49.9 per cent stake in the airline and has spent $7.2bn in the last 15 years to keep Alitalia flying through crisis after crisis.
Under the CAI proposals Alitalia would have merged with Air One, Italy's second airline, employing a total of 12,500 workers.
Pay levels would have stayed the same but employees would have receive seven per cent of profits following an increase in working hours and productivity.
The plan also provided for a foreign airline taking a minority stake in the new Alitalia, while offshoots, such as maintenance and freight operations, would be sold off.