New Jersey’s top health officials estimated that vaccinations could be widely available by April or May, while announcing that police officers and firefighters in the state can start receiving shots on Thursday, the first expansion of the pool of people eligible at this early stage.

More than 450,000 New Jersey residents preregistered to receive the coronavirus vaccine in one day, Gov. Phil Murphy said Wednesday, adding that the high demand for the vaccine is encouraging even though it caused delays and a rough launch for the state’s web portal Tuesday. People who preregister could have a chance at getting shots sooner than the spring — but the state has asked only health-care workers to use the website for now.

The eagerness among many for the vaccine comes as a possible spike in infections looms in the post-holiday weeks. But Pennsylvania is still seeing the fatal effects of the intense preholiday surge, with 368 coronavirus-related deaths reported Wednesday, the highest number in one day since May.

Health officials had expected a potential higher number of deaths this week due to slow reporting during the holidays. Pennsylvania Health Secretary Rachel Levine and other officials have said weeks may pass before the projected surge is fully reflected in the commonwealth’s numbers, and it is too early to know what impact travel and gatherings will have on case counts, hospitalizations, and deaths.

In Montgomery County, the region’s first mass vaccination clinic opened Wednesday, with health-care workers lining up for shots; Pennsylvania State Police said they’d start handing out fliers about the state’s quarantine and mask requirements during routine traffic stops; and federal officials reported that severe allergic reactions to the vaccine were “exceedingly rare” among the first Americans vaccinated.

By the end of the day Tuesday, at least 190,766 doses of the coronavirus vaccine had been administered to people in Pennsylvania, including in Philadelphia. Only health-care workers and nursing home residents and staff are eligible to be vaccinated. A wider group of essential workers and people 75 and older will start getting shots in the next phase, for which the state has said it is still working on plans.

In New Jersey, Murphy and his top health officer said they believed based on conversations with hospital personnel that the number of administered vaccines is being underreported throughout the country and that the state’s count, which stood at nearly 138,000 people vaccinated as of Wednesday, was a “significant” underestimate. Health Commissioner Judith Persichilli attributed part of that lag to the different systems being used between hospitals and other providers to track the doses.

Anyone who preregisters will be kept informed about when they will be able to receive a vaccine, Murphy said.

“By preregistering, you’ll be among the very first to know when the time comes for you to roll up your sleeves,” he said.

On Friday, “mega-sites” for vaccinations will open in Morris and Gloucester Counties. By the end of February, Persichilli said 1,092 clinics will have vaccines.

Eventually, vaccination sites will be linked up to the online portal and people will be able to sign up for appointments at specific locations once they are notified that they are eligible, she said.

New Jersey reported 5,028 newly confirmed cases and 104 deaths. Hospitalization numbers are staying steady, officials said.

In Pennsylvania’s hospitals on Wednesday, about 5,684 patients were being treated for the coronavirus, nearly double the spring peak but slightly fewer than the height of the resurgence last month; 1,148 of those patients were in intensive care units.

The state reported 9,474 new cases — a couple thousand fewer than the record-high daily numbers it was regularly reporting last month but higher than numbers logged during the weeks of Christmas and New Year’s. Philadelphia reported 603 cases and 29 deaths.

Staff writers Laura McCrystal and Rob Tornoe contributed to this article.