Mayor de Blasio said Phase 4 will be scaled down, but includes the restart of TV and film production and professional sports with no fans and higher education. Indoor activities like malls and museums were left out.
Outdoor venues like zoos and botanical gardens may open at 33% capacity.
The rest of the state is already in Phase 4, which typically permits opening malls and certain arts and entertainment centers. Cuomo said the city can't have "any additional indoor activity" because of coronavirus transmission risks.
New York City also has been barred from opening up indoor dining, unlike the rest of the state.
"Not yet," de Blasio said.
"We are still seeing issues, not just in the bars and restaurants, but all across the country. Inside, interior spaces, air conditioned spaces, where the virus is tending to spread. So we will take that precaution in New York City," Cuomo said.
There are now 40 more blocks of Open Streets, including in Chinatown, to help restaurants offer more outdoor dining on Fridays, Saturdays, and Sundays.
On Thursday, Governor Cuomo warned the state would be cracking on bars and restaurants.
Cuomo announced a new "three strikes" policy that will require bars and restaurants to close after they receive three citations for failing to follow rules, including mask-wearing and keeping people six feet apart.
Schools can reopen in Phase 4 regions, but Cuomo has said no decisions will be made until the first week of August.
The National Park Service says Liberty Island will only partially reopen Monday. Ellis Island will remain closed as will the museums on both islands.
WATCH THE SERIES: EYEWITNESS TO A PANDEMIC (Episode 6 below)
Eyewitness to a Pandemic: Episode 6 - To the Streets
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