New Yorkers with chronic health conditions can now sign up for the vaccine.

Starting Sunday, New Yorkers with chronic health conditions like obesity and hypertension can schedule their appointments to get the Covid-19 vaccine at state-run mass vaccination sites. They join a growing number of people in the state who are eligible for the vaccine despite a shortage in supply.

Those who are now eligible include adults who have certain health conditions that may increase their risk of severe illness or death from the coronavirus. Aside from obesity and hypertension, other conditions that would qualify New Yorkers for the vaccine include pulmonary diseases and cancer, Gov. Andrew M. Cuomo announced this month. He also made pregnancy a qualifying condition.

Appointments for people who are in this group can be scheduled for as early as Monday, though most people will probably face a long wait because vaccine doses are scarce now. New Yorkers must provide proof of their condition with a doctor’s note, signed certification or medical documentation, Mr. Cuomo said.

“While this is a great step forward in ensuring the most vulnerable among us have access to this lifesaving vaccine, it’s no secret that any time you’re dealing with a resource this scarce, there are going to be attempts to commit fraud and