The news comes as more and more hospitals cancel vaccination appointments with no new appointments scheduled through Monday.
15 vaccine centers have also closed.
Gov. Andrew Cuomo is blaming the now-former Trump administration for opening up too many categories of eligibility, without increasing supply.
"It should have been opened as you had allocation. Anyway, that is not what we did, it's not what they did. And now you have a period of confusion and anxiety because you're trying to hit seven million people at 250,000 a week," Cuomo said.
Another quarter-million doses will arrive in time for next week, but state officials say that's far from enough.
Some have suggested using second doses, which are in storage, as first doses.
During a visit to a COVID-19 vaccine pop-up site at a NYCHA complex in Brooklyn Saturday, Cuomo said that would only be possible with collaboration from the federal government.
"The reason why the federal government has to agree is because they have to agree that they're then going to send you enough second doses in the future. Otherwise, you want them giving people first dosages and then you don't have a second dosage for them," Cuomo said.
Health experts say administering the second dose of the vaccine within the timeframe outlined by federal guidelines is critical to ensuring long-term protection.
So far more than one million people in the state have gotten their first dose of the vaccine.
At a Friday briefing, Cuomo said deliveries of the week six allocations, about 250,400 doses, are on the way, but those deliveries "are delivered by the federal government by various means and they arrive at different times throughout the week."
The state is able to administer about 80,000 doses per day and could easily do 100,000 per day, Cuomo said.
"The moment the vaccines arrive, our goal is to get them in arms as soon as possible. 250,400 doses per week is not enough," Cuomo said.
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