A New York man was charged Sunday with murder and other crimes in the deaths of his girlfriend and their two young children, police said.

Shane Walker, 36, was arrested after his girlfriend, Alla Ausheva, 37, and their sons, aged 2 and 3, were found dead in their home in Staten Island on Saturday morning, the New York Police Department said in a statement.

Authorities found the mother and children in a house filled with smoke, New York Police Department Assistant Chief Kenneth Corey said earlier. Firefighters extinguished a small fire.

NBC New York reported that Walker and Ausheva were active-duty military service members.

About three hours before the discovery of the dead mother and children, Walker was found walking on the city's Verrazzano Bridge.

Authorities took him to a hospital for evaluation, Corey said.

Corey said police had responded once previously to the address based on a report of a "domestic incident," he said.

"We are in the early stages of an investigation that is ongoing at this time," the assistant chief said.