Metro-North commuters dealt with delays and crowded trains Thursday as they headed to Manhattan, a day after a power line failure disrupted Metro-North and Amtrak train service.

Railroad and utility officials said they were moving closer to restoring some electric power to a vital stretch of the Northeast Corridor north of the city, amid an outage that hampered commuters and intercity travelers through the Northeast.

But Connecticut Gov. Dannel Malloy and executives from Metro-North and Con Edison said it would be days before a patchwork of repairs might return some normalcy to the New Haven Line, which carries 125,000 commuters a day.

Spokesmen for Con Edison, owner of the failed 138-kilovolt feeder line, said the utility was examining whether it could use a system of shunts and transformers to connect power from its distribution network to Metro-North's power system near Harrison, N.Y.

Travelers crowd into a New Haven line train at the Stamford Metro-North Station in Stamford, Conn., on Thursday. Ramsay de Give for The Wall Street Journal

In a news briefing at Grand Central Terminal following a meeting with Con Ed and MTA officials, Mr. Malloy said those repairs would likely be enough to restore partial electric train service at best by the end of the weekend.

"I'm the governor of 125,000 pretty unhappy commuters right now," he said. He again pressed for refunds for affected Metro-North customers, suggesting Connecticut would pursue "legal action" if it wasn't forthcoming.

Metro-North carried half the New Haven line's usual 39,000 morning rush hour riders Thursday, with many diverting to the railroad's Harlem line trains and other travelers heeding calls to carpool or work from home.

Some of those commuters squeezed onto 24 diesel trains that were shifted to serve the New Haven line, or transferred to the Harlem line by bus.

But the strain showed, from crowded Penn Station, where Amtrak ran only regional trains because the Acela express requires electric traction power, to the platform at Stamford, Conn.

"Work is stressful enough; getting to work shouldn't be more stressful," said Robertson Pierre Louis, 28, of Stamford.

The outage occurred at the site of a $51 million power-system upgrade for Metro-North, including the rebuilding of its Mount Vernon East substation to accommodate higher power flows and regenerative braking train cars, which will return energy to the power system.

One of Con Edison's two 138-kilovolt feeder cables—buried, oil-filled pipes that connect the utility's distribution network to Metro-North's power substation—had been disconnected as part of the upgrade project.

At some point, the other feeder cable broke and began to leak the oil that insulates its high-voltage lines, according to Con Edison, and eventually overheated and failed altogether around 5:22 a.m. Wednesday.

Mr. Malloy criticized the decision to rely on a single feeder cable during the power upgrade project and said changes should be made in future phases elsewhere on the line. MTA and Con Ed officials said the feeder cable had been extensively tested and had worked without incident for two weeks before it broke.

Gov. Andrew Cuomo of New York, who has sparred with utilities over their progress in restoring power in the past, defended Con Ed's performance Thursday, saying the company was "doing the best they can."

—Sarah Armaghan and Timothy O'Connor contributed to this article.

Write to Ted Mann at