The New York Police Department flooded the East New York neighborhood with extra officers to assist in the manhunt and reassure frightened residents. Police described the attacker as a stranger who chose the victims randomly.
"This is particularly heinous crime," Police Commissioner William Bratton said. "Two young children in an elevator with no place to escape, nothing at all, and some character gets on and just starts stabbing them? ... (Residents) have every right to be concerned."
He added: "We're going to get this guy."
Before the attack at about 6 p.m. Sunday, the boy and girl had been playing together outside a city housing project under adult supervision. According to relatives and witnesses, they went inside alone to get some ice cream from the boy's sixth floor apartment when they were cornered by a heavyset man in his 20s.
The man used a steak knife to stab each child multiple times, police said. He fled on foot, leaving behind the knife.
Officers summoned to the scene found the boy, Prince Joshua Avitto, in the elevator and the other victim, Mikayla Capers, just outside the building, police said.
Avitto was pronounced dead at a hospital. Capers remained hospitalized in critical condition Monday.
"Thank God, Mikayla Capers is alive," Mayor Bill de Blasio said Monday following a separate event. "She is getting exceptional care. We are hoping and praying she can pull through."
Asked about reports that there were no security cameras in a building located in a neighborhood that's seen a recent spike in violent crime, the mayor said the City Council would get an update on public housing security efforts later this week.
"The bottom line is, Commissioner Bratton was already in the process of moving a substantial number of police in the areas where we've been having troubles," he said.
Police were investigating whether the same man may have fatally stabbed an 18-year-old woman on Friday a few blocks away. A similar knife was recovered at the scene of that slaying.
Brooklyn Borough President Eric Adams offered a $5,000 reward for information leading to the arrest and conviction of the assailant. He warned parents to keep a closer eye on their children "until this sick mind is caught."