Those storms caused some scattered powers outages, mainly in northwestern Westchester.
The latest round of storms should arrive after 2 p.m. Some of the storms could produce damaging winds, with gusts as high as 23 mph.
The showers and thunderstorms in the area could bring rainfall amounts of 1 to 2 inches, with some areas getting as much as 3 inches.
Hourly rain rates could be up to 2 inches per hour, the weather service said.
A Flash Flood Watch, which began at 4 a.m., remains in effect until 4 p.m. Tuesday.
Tuesday night will be mostly cloudy, with a chance of scattered showers and thunderstorms before midnight. Chance of rain is 40 percent.
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