New York’s first tentative steps toward reopening follow other states that have already relaxed restrictions.
Last week, Cuomo said regions of the state could phase in reopening if they met seven conditions.
COVID-19-related deaths and hospitalizations need to trend down and there must be enough hospital beds to meet a surge.
Cuomo gave no indication that New York City or the surrounding areas are anywhere near being able to reopen.
He also reported another 12 cases, for a total of 85, of a newly-recognized, Covid-related illness that afflicts children and has killed three in New York. The condition is called pediatric multi-system inflammatory disease, and it can cause dangerous inflammation, including to the heart.
Earlier on Sunday, New York City Mayor Bill de Blasio also issued a warning about the illness, saying that 38 cases have been detected in the city and another nine are being investigated. One child has died, he said.
The total number of new coronavirus cases in New York rose on Sunday 2,273, for a total of 335,395.
The number of new deaths dropped from 226 the day before, the lowest since March 27, and marked the 10th straight day of new deaths at a plateau in the 200s. New and total hospitalizations, as well as intensive care cases, continued to drop.
Meanwhile, COVID-19 has now infected 4,101,482 people worldwide and 282,700 people have been killed due to this pandemic. Around 1,408,771 people of that tally have recovered.