Saying they wanted a more thorough review of its potential impact on public safety, Los Angeles City Council members Tuesday delayed a vote on a budget-cutting proposal that would have taken selected ambulances out of service for 12 hours at a time.

“There’s nothing that can more directly affect whether someone lives or dies among all the services in our entire budget than ambulance and paramedic services,” City Councilman Paul Koretz said. “I honestly think that is the absolute last thing that we should be looking at cutting.”

The proposal called for taking 10 of the department’s least-used ambulances out of service during the 12 hours of each day when they get the fewest calls.

The move was estimated by the fire department to save about $3.5 million during the last three months of this fiscal year and $23 million in the next.

Under the plan, the 60 firefighters who normally work the overnight shift on those ambulances would be transferred to other fire stations that are short on staff so the department can fill vacancies without paying overtime.

The Fire Department is already working with 15 fewer fire trucks and nine fewer ambulances under the so-called modified coverage plan that went into effect last August to save $39 million this fiscal year.

Councilman Greig Smith said he became apprehensive about the ambulance proposal when the department showed statistics indicating the ambulances would be closed during the hours when they receive about 40 percent of their emergency calls.

“It’s very problematic for me to say to the people in my district or any district in the city that in most cases, we would have an ambulance there, but in a very, very large number — 40 percent — we won’t have an ambulance there,” Smith said. “I don’t know how you moralize that as being sufficient.”

Councilman Janice Hahn told department officials: “Go back to the drawing board, and one more time come back with a way to save $3 million because I don’t think there is the will on this council to close these ambulances.”

“If we’re going to look at efficiencies in ambulance service, low call volume alone can’t be the deciding factor in determining how to re-deploy these resources,” Councilman Paul Krekorian added.

“Among other things, we need to look at impacts on response time; we need to look at distance to provide backup; we need to look at isolation of the stations that have that low call volume; what the traffic patterns are; the demographics of the area; and what the severity of calls are,” he said.

“Those things have to be taken into account in my view as well.”

A “working group” moderated by Smith and composed of the fire and police chiefs, budget and legislative analysts, and union leaders is looking at an alternative proposals to cut costs and raise revenues, including:

• Reassigning 57 staff assistants.

• Outsourcing the task of billing residents for ambulance transport.

• Increasing the fees charged by the fire department for transporting patients by ambulance from the current $1,004 to $1,147 or even possibly $1,500, matching fees charged by other municipalities.

• Imposing a fee for basic services provided at the scene of ambulance responses that do not include patient transportation.

• Asking voters to approve a ballot measure that would let residents pay a fee that would exempt them from paying for emergency medical services or give them a discount.

• Enacting a parcel tax that would pay for fire protection services.

• Imposing additional fees for certain fire department services.

• Postponing the first two firefighter recruit training classes in 2010-11.

• Charging outside agencies for providing their officers with training at the Police Academy.

• Letting the county and federal government lease space for inmates at the new Metropolitan Detention Center.

• And improving the collection of false alarm fees and penalties.