Bloomberg, who is in tense negotiations with municipal workers' unions, said an extra 7,000 jobs would have to go unless major reductions are made in employee benefits.
"We cannot continue. Our pension costs and health care costs for our employees are going to bankrupt this city," he said in comments broadcast on NY1 television.
Bloomberg, running for a third mayoral term at the end of this year, said that proposals from unions so far were "nowhere near what is adequate."
The possible job cuts, first announced Wednesday, would be on top of 1,300 already proposed and another 8,000 that could be axed through attrition.
Department heads have until Monday to propose cuts and Bloomberg must present the city budget by the end of the month. The city is barred by law from running deficits.
The recession and the Wall Street crisis have knocked a huge hole in city finances that traditionally relied heavily on taxes from financial companies.
The budget office on Wednesday said that 7,000 extra job cuts would allow the city to cut a further 350 million dollars in expenditure.