ALBANY, N.Y. – New York, the onetime center of the pandemic, faced a growing crisis on Monday over the lagging pace of coronavirus vaccinations, as deaths continue to rise in the second wave and Gov. Andrew M. Cuomo came under mounting pressure to overhaul the process.

The small number of vaccine recipients is particularly striking in New York City, where roughly 110,000 people — in a city of more than 8 million — have received the first of two doses necessary to help prevent serious cases of the disease. That is about a quarter of the total number received by the city.

The concern over vaccinations in New York echoes problems reported during a sluggish rollout across the nation, and comes as a man in his 60s became the state's first confirmed case of a more contagious variant of the virus. The man was recovering, but Cuomo said early indications were that the case — in the northern city of Saratoga Springs — was evidence of community spread.

"I think it is much more widespread than people know," Cuomo said.

The confirmation of the variant in New York could complicate the planned inoculation of some 20 million residents, with criticism beginning to mount over the rollout. On Monday, Mayor Bill de Blasio called on the Cuomo administration to allow the inoculation of a broader array of essential workers and New Yorkers who are 75 and older.

The governor on Monday authorized a wider swath of health care providers, and others potentially exposed to the virus, to receive the vaccine, including pediatricians and primary care doctors.

Cuomo rejected any notion that his administration was at fault for not distributing more vaccines, asserting that the problem was a local issue, and urging de Blasio and other leaders who oversee public hospital systems to take "personal responsibility" for their performance.

The governor threatened to fine hospitals up to $100,000 — and redirect future vaccines to other hospitals — if they did not rapidly increase the pace of vaccination.

"We want those vaccines in people's arms," Cuomo said, adding, "This is a very serious public health issue."