The number of people who have received their first dose of the COVID-19 vaccine in New York has increased daily since Monday amid a stalled roll out across the country and in the state. 

Gov. Andrew Cuomo on Tuesday announced the vaccination rate has tripled since the start of the week among health care workers. Cuomo has sought to apply pressure on hospitals administering the vaccine at the moment. 

"The vaccination rate has tripled since Monday," Cuomo said. "So I'm glad they heard me."

There are now 2.1 million people who are eligible to receive the first dose of the COVID-19 vaccine in New York, encompassing all health care workers, nursing home employees, and nursing home residents. 

An even larger part of the population will be eligible for the vaccine under the "1b" phase that includes first responders like police officers and firefighters, as well as teachers and people 75 and older. 

Still, Cuomo was hopeful production will be increased among the private sector pharmaceutical companies that are manufacturing the vaccine.

"That's over 6 million in 1b. It takes a long time," Cuomo said. "Flip side, the federal government should be increasing production. They say they will, I believe they will."