Maksim Gelman, 23, allegedly first fatally stabbed his 54-year-old stepfather, Aleksandr Kuznetsov, in the early morning hours at the Sheepshead Bay apartment they shared in Brooklyn borough, police told the New York Daily News.
Gelman then allegedly stabbed his girlfriend and her mother to death in an apartment in the same neighborhood, the newspaper said.
Immediately after killing the women, Gelman stabbed a 42-year-old man and stole his car, police said. That victim was hospitalized in critical condition.
One mile from the carjacking, Gelman struck an elderly pedestrian, who was in grave condition at another hospital.
Gelman is 6 feet tall and weighs 170 pounds, police said.
"We're actively pursuing him," said NYPD Deputy Commissioner Paul Browne, asking anyone with information to call Crime Stoppers at (800) 577-TIPS.