Bloomberg says the city is "in great shape" after the overnight snowstorm.
Bloomberg said New York City can offer equipment and manpower if other communities need help with snow removal.
Bloomberg gave a briefing at a sanitation garage in Queens. He said the Sanitation Department has deployed 2,200 pieces of equipment and will have every street plowed by the end of the day.
He said the city "dodged a bullet" with this storm but winter's not over.
The first inbound passenger flight at John F. Kennedy International Airport landed at 9:30 a.m., according to the Port Authority of New York & New Jersey, which operates the region's three major airports.
Meanwhile, Amtrak said the New York-Boston train route would remain closed Saturday as crews cleared tracks of snow and fallen trees. Trains were running south from New York, and between New York and Albany.
Airports in the Northeast shut down Friday afternoon as a snowstorm of potentially historic proportions blew in. The storm brought more than 2 feet of snow in some parts of New England and left more than 650,000 homes and businesses without power.
These days, airlines try to get ahead of big storms by canceling flights in advance. They want to avoid having crews and planes stuck in one area of the country. They also face fines for leaving passengers stuck on a plane for more than three hours under a rule that went into effect in 2010.
Logan Airport said it expects to open one runway by 11 p.m. Across the region, flights were expected to be back on close to normal schedules on Sunday.
Flight-tracking website FlightAware said airlines have canceled 5,368 flights because of the storm. Airlines have waived the usual fees to change tickets for flights in the affected areas.
Hardest hit was United Airlines. It has cancelled 710 Friday, Saturday and Sunday flights, according to FlightAware.