"If Air France believes in Alitalia, it will participate in the capital increase. If it doesn't, it will give Alitalia and the government the possibility to find an international partner," he said in Milan on the sidelines of a motorcycle trade show.
The comment betrayed tensions over the negotiations between the airlines.
Air France-KLM, which holds a 25 percent stake in the Italian airline, is being urged to join shareholders in injecting more funds as part of a
€300m recapitalisation plan.
The Franco-Dutch airline reportedly responded a week ago by telling Lupi it could do so - but only if Alitalia axed 5,000 jobs, ousted its board of directors and came up with a debt restructuring plan.
However, Air France-KLM has previously denied making any conditions over job losses.
The restructuring conditions have made Alitalia and the Italian government bristle.
Lupi pushed back on Sunday by saying that, if Air France-KLM "decides to dilute to six percent" its stake by not taking part in the recapitalisation,
"I think Alitalia, as a private company, will be forced to find other partners".
The Italian airline is handicapped, however, by €1.2 billion euros in debt and Italy's determination to keep it a flag-carrier.
Alitalia was already bailed out by taxpayers five years ago in a controversial operation that handed a consortium of private Italian companies a majority stake, part of which was later sold to Air France-KLM.
The still-struggling Italian airline is again flirting with bankruptcy, prompting the hasty recapitalisation plan. Italian energy group ENI has threatened to ground its fleet of planes by stopping fuel supplies because of unpaid debts.
Alitalia says Italian banks are lined up to lend it 200 million euros. And the state-owned Italian postal service has been tapped to contribute up to €75m, triggering rivals' allegations of illegal protectionism.