The remnants of a violent storm that claimed 13 lives in Oklahoma sent punishing winds and torrential downpours to the farthest corner of the Northeast and a tornado to the South. And there could be more coming, though meteorologists say the worst is over.

The National Weather Service said the work week could begin with storms bringing showers to the far Northeast and mid-Atlantic and large hail and high winds to the Great Plains.

But it won’t be like Sunday, when storms flattened trees and utility poles in parts of the northern New England, delayed flights in New York City and caused a tornado to touch down in South Carolina.

The weather service issued a rare tornado warning as a line of thunderstorms raced through New Hampshire into western Maine. It said a tornado warning was issued as radar indicated a possible tornado in Maine. The tornado was not immediately confirmed.

By early Monday, more than 12,000 customers were still without power in Vermont, New Hampshire and Maine, down from more than 40,000 outages at the peak.

Weather service meteorologist Bill Goodman said a slow-moving cold front across the Northeast and mid-Atlantic could bring more rain on Monday. “We could get repeat showers over the same areas. It’s a recipe for flooding,” he said.

In north-western South Carolina, a tornado knocked a home off its foundation and blew part of the roof off, said Taylor Jones, director of emergency management for Anderson County. Some trees were blown down and there was heavy rain, but no widespread damage. No injuries were reported.

The stormy weather in the New York City region shortened the Boston Red Sox-New York Yankees game and produced backups at major airports. But by early Monday, delays were down to 15 minutes or less at airports on the East Coast.

In the South, thunderstorms, high winds and hail rolled through as part of a slow-moving cold front.

In Texas, the Coast Guard said its crews saved or helped rescue 17 people caught in storms along the Gulf Coast. Lt. Matthew J. Walter of Coast Guard Sector Houston/Galveston cited “the devastating effects of strong winds and heavy rains” as the reason for three separate boats capsizing.

Meanwhile, residents in Oklahoma cleaned up after the storms there killed 13 people, including three veteran storm chasers. Tim Samaras; his son, Paul Samaras; and Carl Young were killed Friday. The Storm Prediction Center in Norman, Oklahoma, said the men were involved in tornado research.

Authorities said five children and two adults remained missing and aren’t expected to be found alive.

Oklahoma Gov. Mary Fallin toured the damaged areas in El Reno, about 30 miles (48 kilometers) from Oklahoma City. She said the death toll could rise as emergency workers continue searching flooded areas for missing residents.

The state Medical Examiner’s Office spokeswoman Amy Elliott said the death toll had risen to 13 from Friday’s EF3 tornado, which charged down a clogged Interstate 40 in the western suburbs. Among the dead were two children an infant sucked out of the car with its mother and a 4-year-old boy who along with his family had sought shelter in a drainage ditch.

Five tornadoes struck the Oklahoma City metro area on Friday, the weather service said. Ms. Fallin said Sunday that 115 people were injured.

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