New York will lower its age threshold for Covid-19 vaccine eligibility beginning on Wednesday, allowing anyone older than 60 to be inoculated, Gov. Andrew M. Cuomo announced on Tuesday.

“That means people, like as old as I am, will now be eligible for the vaccine,” Mr. Cuomo, 63, said at an appearance in Syracuse.

The state will also expand its eligibility requirement the following week to open vaccination to a large number of public-facing workers, including government employees, nonprofit workers and essential building services workers. Those people can begin to get vaccinated on March 17.

Mr. Cuomo pointed to expected increases in supply from the federal government as the reason behind expanding vaccine eligibility.

Among the workers eligible to get vaccinated next week are public works employees, social service and child service caseworkers, government inspectors, sanitation workers, election workers, Department of Motor Vehicle employees and county clerks.

Appointments will open for people over 60 years old starting at 8 a.m. on Wednesday, Mr. Cuomo said. People over 65 were made eligible for a coronavirus vaccine in January.