Governor Charlie Baker on Tuesday announced a plan to pump $800 million into Massachusetts health care providers, as many struggle financially amid a coronavirus crisis that has now killed more than 350 residents and threatens to strain the system’s limits with a crush of new patients.

The announcement came as the state reported 96 new deaths in Massachusetts due to the outbreak, bringing the total to 356. Health officials said the higher-than-typical daily tally reflected death reports that came in over the weekend but had to be matched with lab-confirmed cases before being released to the public.

The number of confirmed cases climbed by 1,365, bringing the total number to 15,202 — nearly a thousand of them emerging from long-term care facilities like nursing homes, where outbreaks have killed dozens of residents and infected staff in recent days. The day’s new cases emerged from nearly 5,000 new test results, bringing the total tested in Massachusetts to 81,344 people.

The growing number of cases could presage what Baker and public health experts say is a looming surge in seriously ill patients that threatens to overwhelm the health care system.

In response, Baker said, the administration will boost MassHealth hospital funding by $400 million, and distribute another $400 million among nursing homes, community health centers, and other providers between now and July in a bid to shore up budgets that are straining under the demands of the crisis.

“We’re going to almost double our [hospital intensive care] capacity but there’s no money coming in the door for that,’’ Baker said at a news conference Tuesday. “We want to make sure their workforces are prepared clinically. We also want them to be in decent shape financially.’’

Large hospital groups around Greater Boston have begun furloughing employees and ordering pay cuts. Boston Medical Center last week furloughed 700 employees — 10 percent of its workforce — while doctors and other staff at Beth Israel Deaconess Medical Center and South Shore Health have seen pay frozen or reduced.

Most hospitals have cut elective surgeries and sharply curtailed non-coronavirus treatment to make room for the surge of COVID-19 patients, with revenue plunging as a result. Since that came via an order of the state, Baker said, it only makes sense for the state to help hospitals absorb the financial losses.

Much of the $800 million will come from savings MassHealth is seeing by not paying for those elective procedures right now, along with increases in federal reimbursement rates to deal with COVID-19 treatment.

Baker discussed the move with legislative leaders, but said it wouldn’t require a supplemental budget or legislative action because it amounted to “basically moving money around.’’

“We basically told the health care community that does elective surgeries to stop because we wanted them to build out capacity for COVID-19 and that’s exactly what they’ve been doing,’’ he said. “As a result there’s been a pretty significant drop in payments for those activities.’’

The rest — more than $300 million — will be spread around a wide array of providers, from primary care doctors to personal care attendants, who are keeping residents safe and out of the hospital.

“It’s a big investment in our health care system,’’ Baker said, adding that the money will help to make sure providers can operate “all these things we need right now.’’

At a City Hall news conference earlier in the day, Boston Mayor Martin J. Walsh said hospitals will need more morgue capacity in the coming days, as he warned that the expected peak of the pandemic is still ahead. He urged people to continue social distancing.

“The next few weeks are going to be a test of our health care capacity like never before,’’ Walsh said. “Unfortunately, we’re going to see a lot more loss of life.’’

He said the city would help hospitals to expand their morgue capacity, including by expediting permitting.

“These facts are an unsettling reminder of how serious this emergency is,’’ he said.

In a nod to the importance of those working on the front lines, Walsh announced that health care workers who receive parking tickets will have their fees waived by e-mailing a photo of their ticket and their hospital ID to parking@boston.gov, unless they’re ticketed for parking in front of hydrants or in handicapped spaces without a placard.

The pandemic appears to have taken a toll on the city’s first responders. As of Tuesday, 45 Boston firefighters were self-isolating because of a potential exposure to a COVID-19 case, said Brian Alkins, a department spokesman. To date, that department, which has 1,400 members, has had 15 firefighters test positive for the coronavirus.

Boston EMS, meanwhile, has 25 of its members out because of exposure or illness linked to COVID-19, said Caitlin McLaughlin, an agency spokeswoman.

That department has had eight workers test positive so far. Some of them have returned to work, said McLaughlin, but she did not have a specific number of those who have recovered.

At the Boston Police Department, Sergeant Detective John Boyle said there have been 52 confirmed COVID-19 cases among the sworn officers, while seven civilian workers were also confirmed cases. Like EMS, some of the individuals who were confirmed cases have returned to work.

Walsh emphasized that the disruption to people’s lives is far from over. Boston Pride events scheduled for June have been postponed a year, organizers said, putting its 50th anniversary celebration on the shelf.

“This is going to go on for a substantial amount of time,’’ Walsh said.

He urged residents to wear masks to slow the spread of the virus — guidance he said he is also following, donning a mask when he walks outside his office in City Hall.

Martin Finucane and Jaclyn Reiss of the Globe staff and Globe correspondent Matt Berg contributed to this report.