3 daughters, parents of NYC ad executive killed in Stamford, Connecticut house fire (VIDEO)

The five people killed in a Connecticut house fire on Christmas Day have been identified as the three daughters and parents of a New York advertising executive.

According to the Associated Press, Madonna Badger's daughters — a 10-year-old and 7-year-old twins — and her parents, visiting for the holiday, were killed when her Victorian house was engulfed by flames shortly before 5 a.m..

Badger and a male acquaintance were able to escape from the house. She was treated at a local hospital and discharged.

Firefighters who were unable to save the five were "suffering" as a result, Stamford's mayor told the media late Sunday.

"It is a terrible, terrible day for the city of Stamford," Mayor Michael Pavia told reporters at the scene of the fire at 2267 Shippan Ave., which The Associated Press described as "a tony neighborhood along the Connecticut shoreline."

"There probably has not been a worse Christmas day in the city of Stamford."

Two people survived the three-alarm fire, which drew several fire crews from surrounding towns, said Acting Fire Chief Antonio Conte, adding that their condition was not known.

Conte said firefighters were pushed back by intense flames and heat when attempting to reach the victims, the Hartford Courant reported.

"We just couldn't get to them," Conte said, adding that the first responders "frankly are suffering as a result. Our heart goes out to them."

Badger, the AP wrote, founded the New York City-based ad agency Badger & Winters Group, which operates in the fashion industry.

The AP quoted neighbor, Sam Cingari Jr., as saying that he was awakened by the sound of screaming and that the house was entirely engulfed by flames.

"We heard this screaming at 5 in the morning," he said. "The whole house was ablaze and I mean ablaze."

Conte said fire marshals might take several days to discover the cause of the blaze.