Service was restored around 11:30 a.m., Amtrak spokesman Cliff Cole said, but residual delays were expected at least through late afternoon.
The problem occurred in North Bergen, N.J., where trains go under the Hudson River en route to Manhattan.
A low-voltage reading originated from that spot, leading Amtrak to suspend service in and out of New York and to idle other trains, Cole said.
Trains can continue running in such circumstances but are routinely moved to the nearest station to avoid the possibility of a larger power failure caused by trains operating normally at low voltage, he said.
Amtrak was investigating what caused the low voltage reading. Cole said that there was no indication it was caused by human error, but that extreme weather conditions can affect the electrical system.
The weather across the region Wednesday morning was seasonally cold but mostly clear.
Wednesday's stoppage stranded thousands of travelers on trains and in stations from Boston to Washington, D.C. Some commuters in New York and New Jersey were able to switch to subway trains in and out of the city, but others weren't as fortunate.
At Penn Station in New York City, travelers packed a waiting area, sitting on suitcases with bags of holiday gifts scattered around them on the floor. A display board showed grim news for every train.
Lyn Hunt and four family members had been traveling since Saturday - or trying to. Their trip to Newark from England had to be rerouted through Chicago because of the snowstorm that swept up the East Coast over the weekend.
The family then traveled by Amtrak from Chicago to New York, only to be delayed again Wednesday as they tried to take a train north.
"We've decided that our motto is adapt, improvise and overcome," Hunt said. "We don't know yet how we will adapt or overcome this."
Her answer came just before noon when an announcement crackled over the loudspeaker that power had been restored and trains would begin rolling again.
At Washington's Union Station, at least one train was announced as canceled and some passengers said they were told by Amtrak personnel that the problems were related to cold weather.
Nicole West-Burns, who was getting off a southbound train, said Amtrak told her and other passengers getting on in Philadelphia on Wednesday morning that the doors were frozen shut.
At Philadelphia's 30th Street Station, trains were delayed one to almost three hours, and frustrated holiday travelers gathered throughout the station.
Ginny Sciabbarrasi, 30, stared gloomily at the board as she waited for her train to Lancaster, Pa., having already endured a flight from Denver.
"I caught the redeye from Denver this morning, and now I don't know when my train is going to leave," Sciabbarrasi said. "I'm not very happy with New York at the moment."
The delays came days after Amtrak sent out a news release touting its efficiency in moving travelers during last weekend's major snowstorm in the same region.
"Over the weekend Amtrak carried thousands of people to their destinations when others couldn't - and we did so safely," the release reads. "We accommodated numerous travelers who gave up on the airlines. ... Amtrak stepped up, met the challenge, and once again proved to be a vital transportation link."
Contributing to this report were Associated Press writers Sara Kugler in New York, Patrick Walters in Philadelphia and Sara Karush in Washington, and photographer Jacquelyn Martin in Washington.