Mayor Bloomberg will earmark $575 million to help the city’s public hospital system get out of its financial hole, city officials said yesterday.

The money, to be included in a “budget modification” being released tomorrow, will be used to plug a $250 million budget deficit at the Health and Hospitals Corporation this year and to offset expected shortfalls next year, a spokesman for the mayor, Jordan Barowitz, said.

While the city was expected to float a cash infusion to keep its 11 public hospitals in business, the $575 million, which will be matched by the federal government, is more than had been planned.

The HHC bailout, one of several over the past few years, highlights the depth of the fiscal troubles of the public hospital system, and the depth of Mr. Bloomberg’s support for it.

It is one of several new initiatives the mayor is adding to the city’s ledger this week. He also will make official the first of two $1 billion contributions to a new health care trust fund for city retirees that he announced in his preliminary $55.5 billion budget.

In addition, the “modification” will allocate $100,000 to the city clerk’s office to ramp up enforcement of lobbying laws and will add money to help libraries and cultural institutions.

The latter will be a financial “swap” in which the libraries and institutions put in the money they’ve raised toward operating their facilities and the city steps in to help defray the costs of construction projects, Mr. Barowitz said.

The chairman of the City Council’s Finance Committee, David Weprin, characterized the library money as an olive branch because the new council speaker, Christine Quinn, has said she wants to change the annual budget “dance” in which the council fights for money it knows will be restored in the end.

“I think it’s a gesture in the right direction,” Mr. Weprin said. “We’ve made it a priority that we want to stop the game playing, and I think the mayor feels the same way.”

The City Council, which is scheduled to unveil its response to Mr. Bloomberg’s preliminary budget on Thursday, already has said it will be request more than $9 million for 18,000 new bulletproof vests for police officers.

Mr. Weprin said the council is working on the rest of its response, but that it is “considering” tax-cut proposals.

He did not specify which taxes would be targeted, but others, including council members David Yassky and James Oddo, have suggested slashing both the unincorporated business tax, a levy on small-business operations, and the utility tax.

“It’s certainly should be something that they consider, particularly the unincorporated business tax, because it makes it harder for entrepreneurs to thrive here,” a senior fellow at the Manhattan Institute, Nicole Gelinas, said. “So many of the other states and cities that we compete with don’t have a state income tax at all.”

There is no indication that Mr. Bloomberg is planning those kinds of tax cut for fiscal year 2007, which starts on July 1.

Budget experts said Mr. Bloomberg has made a habit out of keeping to the broad outline of his preliminary budget and adds new initiatives only when the city’s fiscal picture drastically changes midway through the budget season.

Several budget groups also praised Mr. Bloomberg for stashing away surplus money rather than increasing spending, which would have been more politically popular. Mr. Bloomberg said that because of the projected deficits, the $3.3 billion surplus should not go toward tax cuts.

“I don’t think anybody with any sense of fiscal prudence would argue you shouldn’t worry about something that is only a year and a half or a year and five months away,” he said when he unveiled his budget in February.