AUSTIN, Texas — Widespread power outages in the Texas capital stretched into a third day Friday for thousands of residents following a winter storm that was spiraling into a management crisis as city leaders remained unable to say when all the lights would come back on.

Impatience among frazzled, freezing and fed-up families in Austin escalated even as milder weather returned. On Friday, the newly elected mayor stood before cameras and apologized after a week of slow repairs, failed technology and lacking communication with the public.

“The city let its citizens down. The situation is unacceptable to the community, and it’s unacceptable to me,” said Mayor Kirk Watson, a Democrat who took office in January. “And I’m sorry.”

While New England began shivering and closed schools under an Arctic blast expected to bring the coldest weather in a generation, temperatures finally started to moderate Friday and bring some relief to Austin, where at any given time about 30% of customers in the nation’s 11th-largest city have been without electricity since the ice storm swept into Texas late Monday.

City officials said Friday that significant progress was finally being made as frozen equipment and roads thawed. About 117,000 customers still lacked power, according to Austin Energy, the city’s utility. That’s down from a peak of around 170,000 people, nearly a third of all customers.

But frustration was not melting away for residents who still had no assurances or sense of when their power would return.

For many, the outages stirred unpleasant memories of the 2021 blackouts in Texas, when hundreds of people died after the state’s power grid was pushed to the brink of total failure because of a lack of generation. That was not the case this week, as the grid maintained sufficient reserves.

Energy experts said Austin’s dense tree canopy made the outages caused by fallen trees and iced-over power lines more widespread. Most power lines are overhead, and Austin officials said burying existing lines would be expensive and more difficult to repair.