The National Weather Service said Tuesday morning that it was expecting heavy snow from eastern Pennsylvania through New York and into New England for much of the day. By the afternoon, snowfall totals topped a foot in parts of New York, New Jersey, Connecticut and Massachusetts.

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Public officials across the Mid-Atlantic and Northeast pleaded with people to stay off the roads, asking them to keep streets clear for first responders. They urged travelers to take public transit, though a number of systems — including Amtrak as well as New Jersey Transit and New York subways and commuter rails — reduced service as the storm approached.

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Airlines canceled more than 6,000 flights on Tuesday, according to FlightAware.com, the bulk of them scheduled for airports in the New York, Boston, Philadelphia and Washington areas. In Philadelphia, most airlines canceled all service through the airport there on Tuesday. New York state officials said that 99 percent of flights through LaGuardia Airport and two-thirds of flights at John F. Kennedy International Airport had been scrapped.

The snowstorm interrupted daily routines for millions of people, closing public schools in New York, Boston and Philadelphia for the day and keeping many workers at home. Snow totals in some areas appeared likely to fall below forecasts, including in New York City, where the blizzard warning was downgraded midway through Tuesday morning.

While the storm was an apparent dud in New York, with just a fraction of the projected snowfall actually arriving in the heart of Manhattan, there was considerable snowfall elsewhere.

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In New York, 7.2 inches fell at Central Park by 2 p.m.,the National Weather Service said, even though some forecasts had called for as much as two feet there. But the storm delivered steady snow in other areas, hitting 13 inches in Mahwah, N.J., just outside Manhattan; 15 inches in Burlington, Conn.; and 17 inches in Warwick, N.Y.

New York Gov. Andrew M. Cuomo (D) said he called up 2,000 National Guard troops to move across the state in response to the storm. He also announced a travel ban in Broome County, which includes Binghamton and borders Pennsylvania.

Cuomo said that officials had originally deployed based on the forecasts saying New York City and Long Island would be hit particularly hard, though he said the storm wound up shifting to the west.

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“Mother nature is an unpredictable lady, sometimes,” Cuomo said during a briefing Tuesday morning. “She was unpredictable once again today.”

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Looking ahead to Wednesday, school officials in New York City said they expected all schools would reopen there.

Aboveground subway service in New York was suspended at 4 a.m., while Metro-North trains were set to stop running at noon, the Metropolitan Transportation Authority said.

The National Weather Service said that a blizzard warning remained in effect in eastern Pennsylvania and northern New Jersey until Tuesday evening, saying that up to two feet of snow is possible there. A similar warning is in place through midnight in Connecticut and parts of northeast New Jersey.

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Pennsylvania Gov. Tom Wolf (D) said he is calling up nearly 700 Pennsylvania National Guard troops to help move emergency workers and check on stranded drivers.

Connecticut Gov. Dannel P. Malloy (D) banned travel on state roads starting at 5 a.m. on Tuesday and lasting “until further notice,” with exceptions only for vehicles involved in emergency response or storm recovery operations. Malloy asked his state’s residents “to make safety a priority and to not make any attempt to travel.”

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In Massachusetts, forecasters called for up to a foot of snow in Boston through the day and as much as 30 inches in western parts of the state. Gov. Charlie Baker (R) told his nonemergency employees not to come to work on Tuesday, and his office asked people to avoid “unnecessary travel” during the storm.

This story, first published at 10:30 a..m., has been updated through the day.