The death toll from a fierce winter storm that gripped much of the United States over Christmas rose to at least 61 on Thursday, officials said.

Erie County executive Mark Poloncarz said two more deaths had been reported in the western New York region that bore the brunt of the historic storm, bringing the total to 39.

Erie County includes the snow-battered city of Buffalo, where most of the deaths occurred.

Poloncarz said 17 of the 39 victims were found outside, 11 were in homes, four were in cars, four died while shoveling or snowblowing and three were the result of an inability of emergency responders to reach them in time.

Nine deaths were reported in storm-related car crashes in the midwestern state of Ohio with scattered fatalities in at least half-a-dozen other states.

With temperatures rising and snow melting, officials in New York had expressed concerns about flooding but the county executive said "it does not appear like it will be bad."

"Thankfully, it appears that flooding will be minimal," Poloncarz said.

He said that electricity had been restored to all county residents.

As Buffalo dug itself out of the once-in-a-generation storm, there has been mounting criticism of the response of the authorities with Poloncarz calling the city's handling "embarrassing."

A travel ban, for example, was not issued in Buffalo until 9:30 am on Friday morning when many people were already on their way to work.

The storm also brought unseasonably cold temperatures to states such as Texas and Florida and caused chaos at airports, with thousands of flights delayed or canceled.

Southwest Airlines, which canceled more than 15,000 flights in eight days after what it said was a breakdown in its scheduling systems, said it expected its operations to gradually return to normal Friday.