Non-essential businesses and public and private schools in nine areas in New York are to be closed as authorities try to curb a rise in coronavirus infections, Mayor Bill de Blasio announced on Sunday.

The nine areas are in the boroughs of Brooklyn and Queens and have a testing positivity rate of over three per cent over a seven-day period.

The areas include parts of Far Rockaway, Borough Park, Midwood, Gravesend, Bensonhurst, Sheepshead Bay and Kew Gardens.

"Today, unfortunately, is not a day for celebration. Today is a more difficult day," De Blasio said.

De Blasio further described another 11 areas as a "real concern" adding that "there does not have to be a second wave."

De Blasio's plan, which is due to start on Wednesday, however, must be finally approved by Governor Andrew Cuomo. The announcement marks the first major reversal of the city and state's phased reopening process.

Cuomo, meanwhile, said the state will assume direct enforcement in 20 areas identified as hot spots around the state that are driving infections to their highest point since the lockdown.

(With input from agencies)