Having adopted a $6.7 billion budget for next year, Los Angeles City Council members said Tuesday it is up to the city's labor unions to determine the scope of any layoffs and furloughs for municipal workers.

The budget adopted Monday stipulates the layoffs of up to 761 workers - with the possibility of 1,000 more if revenue slides - plus 16 to 26 unpaid furlough days, beginning July 1.

But council members and Mayor Antonio Villaraigosa made it clear that the unions can avert many of the layoffs and furloughs if they are willing to make $110 million in contract concessions.

"This is a much stronger budget than we had last year," council President Eric Garcetti said. "It provides more detail on what we are able to afford and the next step is up to the unions."

In its final form, the budget was little changed from the plan proposed by Villaraigosa in April. The mayor's staff was reviewing the final version on Tuesday and had no comment.

But on Monday, the mayor sent a letter congratulating the council on its work and warning that it will take union concessions to keep municipal workers on the payroll.

"If our partners in labor commit to real, structural cost-savings - including fundamental reform of the city's sworn and civilian pension systems - I will support a pathway to restoration of critical city services and long-term financial integrity," the mayor wrote.

Labor leaders, particularly those governing the 22,000-member Coalition of City Unions, remain skeptical of the city's financial projections.

They have proposed an alternative financial plan that would fund a full work force and avoid furloughs through such cost-saving measures as reducing city contracts and controlling bad debts.

City officials have said most of those proposals are impractical or have already been included in the city budget.

"I guess it depends on who you want to believe and what (budget) memo is out there," said Bob Schoonover, president of Service Employees International Union, Local 721.

"The bottom line for us is we started off in January with a $600 million hole and now we're down to $100 million. There are numbers floating all over the place.

"We are going to continue to find a way to do this without further devastating the work force," he said. "We are already at 1997 levels of workers and now they want to add another 700 or 1,700 (layoffs) on top of that? We think there's a better way."

The $6.7 billion budget maintains a 9,963-officer police force, but reduces nearly every other city program, from tree trimming and pothole repair to parks and libraries.

Councilman Bernard Parks, chair of the council's Budget and Finance Committee, said this year's budget required officials to make hard choices.

"Our decisions do not hinge on what someone else is doing. If we don't have the money, we will have to go to layoffs and furloughs."

Councilman Richard Alarcon, the only member who voted against the budget, concurred with Schoonover and other union leaders.

"I still believe that layoffs, furloughs and service cuts are not necessary," Alarcon said. "I believe we can close the gap and keep city services."

Part of the Alarcon solution rests with the Department of Water and Power, which he said can transfer an additional $20 million to the city general fund. The city-owned utility has already transferred $220 million.

"I think we have put too much emphasis on the unions. I think unions have to be part of solution, but I felt there has been an attitude of trying to force the unions to do more when they have been very cooperative."