LOS ANGELES (AP) — Mayor Antonio Villaraigosa backed down from his hardline stance over the budget crisis Wednesday, admitting he cannot shut down city services without the City Council’s approval and requesting $20 million from the power utility to keep the city solvent.

The mayor’s plan to shut down services that don’t make money, such as parks and libraries, for two days a week starting Monday is a ‘‘plan of last resort,’’ said his deputy chief of staff, Matt Szabo.

‘‘We understand that we need to work with the council if, in fact, we would need to implement such a plan,’’ Szabo said.

‘‘But we have to have a final contingency plan that we’re not going to run out of money.’’

The statements capped a day of ramped-up pressure on the mayor from the City Council, the controller and labor unions after he announced Tuesday that he was going to furlough about 22,000 city employees two days a week because the city will run out of cash next month.

The City Council’s chief legislative analyst, Gerry Miller, told councilors Wednesday that the mayor cannot shut down city services without council approval.

‘‘The mayor does not have the unilateral authority to do that,’’ Miller said.

The city also would be violating labor contracts, which stipulate no furloughs, said Bob Schoonover, president of the Service Employees International Union Local 721, which represents about 10,000 city employees.

Villaraigosa and the council are in a political tug-of-war over rate hikes requested by the Department of Water and Power, which is controlled by the mayor.

After the council approved a smaller rate hike to cover increased costs of coal and natural gas, the DWP reneged on a previous promise to transfer $73 million to the city’s general fund, saying without the higher rate hike, it could not afford to give the money.

The council responded by asking the mayor to press the DWP for the funds since he appoints the utility’s board of commissioners and general manager, but he proposed a service shutdown.

On Wednesday the former DWP commission president Nick Patsaouras filed a lawsuit in Los Angeles Superior Court to force the utility to fulfill its obligation to make the transfer. The suit states that the DWP already has an 8 percent surplus, enough to provide the money. Patsaouras stepped down from the commission in October 2008.

Villaraigosa went on a media blitz Wednesday, appearing on CNN, Fox Business News and local radio to explain his shutdown move. ‘‘On May 5, we’ll be out of cash,’’ he said on CNN. ‘‘If I don’t do these actions now, we won’t be able to pay the bills.’’

He later announced he would ask the DWP for $20 million but warned that its board may not approve the transfer.

Szabo said the DWP may be more likely to approve the transfer if it can reach a compromise on the rate hike with the city council. He called the council’s smaller rate hike ‘‘a reasonable compromise’’ but added that DWP must have flexibility to adjust rates in the future in line with its costs.

The council and controller also ratcheted up pressure on the DWP.

Controller Wendy Greuel announced an audit of the utility to verify its claim that it was financially unable to give the city $73 million.

‘‘I want to take the politics out of this process and provide an independent review of the DWP’s finances,’’ she said.

Meanwhile, the council passed a series of motions to wrest control of the DWP away from the mayor.

The council wants to ask voters next year to give it the power to remove the DWP general manager and commissioners. The council also wants voters to decide if it can control rate increases and the DWP budget.

The city has started to feel the effects of its financial trouble. Moody’s Investor Service on Wednesday slashed the city’s credit rating on its debt obligations to ‘‘Aa3’’ from ‘‘Aa2’’ with a negative outlook that means the rating could be lowered further. ‘‘Aa3’’ is Moody’s fourth-highest rating and is considered high-quality.

Another quagmire looms. Greuel said the city would not be able to make payroll May 5 and requested the council transfer $90 million from the city’s reserves to see it through the end of the fiscal year. Using that money, however, would drain the city’s contingency fund.

Szabo said Villaraigosa will continue to seek solutions.

‘‘The mayor has said that he is not going to allow the city to run out of money, nor is he going to ask city employees to come to work if he knows we don’t have the funds to pay them,’’ Szabo said.