Prime Minister Paolo Gentiloni said he had been disappointed by staff's rejection of a rescue plan involving deep job and salary cuts, and reiterated that the state could not and would not step in.
"The truth is what I said before the vote and what I say again today: the conditions are not there for Alitalia to be nationalised," Gentiloni said.
Transport Minister Graziano Delrio meanwhile said the company would be "sold to the highest bidder" and the government made favourable noises about the mooted possibility of a partial takeover by Germany's Lufthansa.
The loss-making national carrier's future is up in the air after its workforce rejected a restructuring plan which management had presented as the only alternative to bankruptcy.
Etihad Airways, which owns a 49 percent stake in Alitalia, and other shareholders had made staff acceptance of the plan a precondition for their participation in a two-billion-euro recapitalisation plan involving a combination of loans and new shareholder financing.
But despite earlier proposals being watered down in negotiations with unions, over two thirds of staff voted to reject them in a ballot on Monday, in which more than 90 percent of employees took part.
The latest draft of the restructuring plan involves eliminating 1,700 jobs from a global headcount of 12,500 and wage cuts of up to eight percent for some of the remaining staff.
The company's board on Tuesday asked the government to appoint administrators to find a purchaser or organise the winding up of the company.
"The most plausible outcome is that we are moving to a brief period of extraordinary administration which could conclude in six months with a partial or total sale of Alitalia's assets," said Economic Development minister Carlo Calenda.
Phoenix from the ashes?
Delrio added: "The business will be sold to the highest bidder ... but Alitalia has been weakened by the outcome of the ballot and its competitors will not give it any gifts."
Asked about the Lufthansa rumours, Delrio said the government was not opposed while Calenda described the possibility as "interesting to explore".
Calenda said the government would seek EU permission to lend Alitalia 300-400 million euros of working capital to keep its planes in the skies for the next six months pending a sale.
Economists have warned Alitalia going out of business could destroy some 20,000 jobs when the impact on sub-contractors is added to that on directly-employed staff.
But the government is reluctant to inject any more taxpayers cash into what consumers group ADUC recently called a "bottomless pit" for public funds.
Calenda said the government had already pumped some 7.4 billion euros into the company, which was rescued from bankruptcy in 2014, when Etihad acquired a 49 percent stake.
Another consumer rights group Condacons has urged the government to guarantee tickets already sold will be reimbursed if Alitalia is grounded, which the state seems willing to do.
John Strickland, an independent airline consultant based in London, said there was a real chance of Alitalia going under.
"It has led a charmed life and had numerous near death experiences," he told AFP. "Whether they will rise like a Phoenix from the ashes again seems less likely at present."
Alitalia has been loss-making for years and has been squeezed hard recently by the emergence of leaner, low-cost rivals on domestic and European routes, particularly Ryanair, which is now the market leader in Italy.
Alitalia lost 460 million euros last year and a similar loss is predicted for this year. The restructuring plan envisaged a return to profitability by 2019 and a subequent expansion of long-haul operations.