New York will allow people 65 and older and those with pre-existing health conditions or who are immunocompromised to be vaccinated against coronavirus, meaning that more than 7 million state residents are now eligible for immunization, Governor Andrew Cuomo said on Tuesday.

Cuomo announced the new policy during a call with reporters. The relaxed restrictions come in response to new anticipated guidelines from the federal government designed to speed up the vaccine rollout.

"We are going to accept the federal guidance," he said.

But the governor expressed skepticism about the new strategy, saying that the federal supply of vaccines was bound to run out in the face of increased demand. The state currently gets about 300,000 additional vaccines per week.

"I don't understand how you can have 7 million people chasing 300,000 vaccines every week and not have everyone be oversubscribed," he said.

And the 7 million people cited by Cuomo do not include those who fall into the category of those who are immunocompromised, which Cuomo said the state is working on coming up with an estimate for.

Cuomo has been criticized for an overly restrictive vaccine rollout, resulting in reports of some providers throwing out unused vaccines.

On Monday, after pressure from local elected officials, the state began allowing shots for people over 75, police, firefighters and teachers.

Mayor Bill de Blasio on Tuesday said that the state had confirmed that grocery workers and shelter workers could also now receive vaccination. He said he was urging the governor to allow food delivery workers to be vaccinated as well.

For more than a week, the mayor has pressured Cuomo to expand the state's vaccination criteria, saying that local officials need the "freedom to vaccinate." As part of his plan, de Blasio has rolled out scores of vaccine hubs as well as mass vaccinations sites that will operate 24/7.

On Tuesday, de Blasio said that the owners of Citi Field, the home of the New York Mets, had agreed to serve as a 24/7 vaccination site. Scheduled to open later this month, the Citifield site will have the capacity to vaccinate 5,000 to 7,000 people a day.

Another 24/7 vaccine site opened Tuesday at 125 Worth Street in Manhattan. It will be followed by two locations in Staten Island and one in Corona, Queens.

But even as the state and city seek to hasten the pace of vaccinations, some were criticizing the plans as poorly executed and plagued with technical problems.

Those seeking to set up appointments through the city's providers have been forced to submit to a multi-step verification process to set up an account and about 51 questions or fields to check off on the Health Department's site.

The city and state have both set up telephone hotlines to make appointments but users have complained of being kept on hold for hours.

As of Tuesday morning, the city has administered 239,000—or 36%—out of the 669,000 vaccine doses it currently has.