On Sunday evening, Gov. Philip D. Murphy of New Jersey said that he too would begin to lay out a vision for reopening his state, which has also lost thousands of lives to the coronavirus. “The road back will be driven by data, science and common sense,” Mr. Murphy said in a tweet.

In New York, the daily count of new cases statewide has generally been trending downward, though the numbers have sometimes varied significantly from day to day and they rose toward the end of last week. Another metric laid out by the White House is the percentage of tests that are positive; by that metric, New York has been on a downward trajectory.

In his remarks, Mr. Cuomo made clear that the road to reopening was cratered with potential hazards, specifically saying there should be no events or attractions that would draw people from more infected regions to less infected areas, such as Central New York or the Adirondacks, two areas he suggested were places where restrictions could soon be eased.

“It’s possible that you open something in Syracuse or you open something in the North Country, where you now see license plates coming in from Connecticut, New Jersey, people from downstate, all coming to that area, because they’ve been locked down and they’re looking for an activity,” he said. “So that’s something that we have to pay attention to.”

At the same time, Mr. Cuomo pleaded with local officials — particularly in the New York City region — to consider how to provide for summer activities for residents, including children. New York’s mayor, Bill de Blasio, has already said that the city’s public swimming pools will not open this summer, even as its playgrounds remain shut for the time being.

“You can’t tell people in a dense urban environment all through the summer months, ‘We don’t have anything for you to do,’” Mr. Cuomo said, adding, “There’s a sanity equation here.”

Earlier on Sunday, Mr. de Blasio had struck a similar chord while announcing a series of advisory groups to help imagine New York City’s future, with an emphasis on a rebuild that “confronts deep inequities” in low-income and minority communities, a theme Mr. Cuomo also touched on.