Swissair was already in trouble before the 11 September attacks
Under the deal, Swissair's flight operations will be taken over by its regional subsidiary Crossair, while other parts of the group will seek bankruptcy protection.
Swissair chairman and chief executive Mario Corti emerged from crisis talks on Monday to say the airline would sell the 70% stake it currently holds in Crossair to Swiss banks UBS and Credit Suisse.
Mr Corti blamed the suicide airliner attacks in the US on 11 September for causing billions of Swiss francs in costs for the cash-strapped group.
But the company was already struggling under a mountain of debt caused by a failed expansion strategy, before the US tragedy.
Flight operations saved
The banks' offer, of 1.36bn Swiss francs (£569m; $840m), only applies to Swissair's flight operations.
Non-flight operations including catering, airport retailing and ground services are in line for the chop, jeopardising thousands of jobs and rendering Swissair stock virtually worthless.
Mr Corti said there was likely to be 2,560 job cuts, 1,750 of them in Switzerland, and SAirGroup and the SAirLines and Flightlease divisions would seek creditor protection.
The combined Swissair/Crossair fleet will be reduced by 24 aircraft, the chief executive of Crossair and head of newly-formed Swiss Airlines, Andre Dose said on Monday.
He said the long-haul fleet would be reduced to 26 aircraft from 35, while the European fleet would be scaled back to 26 jets from 41.
'No alternative'
The deal saves Switzerland's banks from accusations that they allowed one of the country's most high-profile businesses to go out of business, analysts said.
"I do not think there is much of an alternative under current circumstances," Nicholas Van den Brul, airline industry analyst at BNP Paribas in London said.
Switzerland's federal government - which holds a 3% stake in Swissair - said it will not take a stake in the new airline.
"An intervention of the (Swiss) confederation is not necessary," said Swiss Vice President Kaspar Villiger.
"The creation of a new company is the best solution for the future under the given circumstances."
But Credit Suisse still wants the federal and regional governments to take up a 30% stake in the new Crossair.
Guaranteeing flights
Earlier on Monday, Swissair said it was unable to guarantee flights for the rest of the week.
Callers to the Swissair booking line were told the carrier could not confirm that passengers with flights booked this week would be able to fly.
But booking agents said Swissair hopes to be able to provide its scheduled service and advised passengers against making alternative bookings with other airlines.
Swissair hopes to provide more information Tuesday, callers were told.
Sabena repercussions
The rescue deal will have serious repercussions for Belgium's troubled national carrier Sabena, which Swissair jointly owns with the Belgian government.
Sabena grounded more than a quarter of its flights on Monday as a pilots' strike went into a fourth day in protest against plans to restructure the ailing Belgian airline.
Swissair said it was incapable of injecting around 200m Swiss francs into Sabena this week, as agreed under a rescue plan with the Belgian government.
In a reply to a question on whether it was right to assume that the payment had not been made, Mr Corti said: "That assumption is correct."
Both the Belgian state - which said Swissair's decision was a "flagrant violation" of pre-existing agreements - and Sabena said they could go to court if Swissair does not live up to the agreement.
Mr Corti said payments of more than 100m francs due to former French partner airline Air Littoral could also not be made.
"The payments to France have the same status as the payments to Belgium," he said.
In Brussels, Sabena said it would continue its operations.
Trading is Swissair shares has been suspended until the evening of 2 October.