A murder investigation is ongoing
Officers, along with an ambulance crew, found twins in the house - a boy and girl, both aged one, with serious injuries.
The children were taken to an east London hospital but the boy died just before 1am Sunday, whilst the girl remains in a critical condition.
In a statement, police said: "Detectives are urgently trying to trace a man who was at the flat shortly before the injured children were found, but left before emergency services were called.
"The man has not been seen since this time."
Detectives from the Homicide and Major Crime Command have launched a murder investigation and say the incident is believed to be domestic, but no arrests have been made so far.
Police appealed for anyone who knows where Bidhya Sagar Das is to contact them by phoning 999 immediately.
Mr Sagar Das is understood to have worked at a nearby hotel, but a colleague told Sky News that he had been absent for the last two weeks.
A National Police Air Service helicopter tweeted that it was helping "officers searching Finsbury Park for a suspect", and a spokesman said they were "assisting officers from Hackney after two children were found seriously injured at an address in Wilberforce Road, N4".
The family of the boy has been told of his death, but has not yet been formally identified and a post-mortem examination will be scheduled shortly.
A woman living opposite said she had heard a woman shouting last night and opened the window to offer help.
"I was watching TV," she said. "I heard someone was shouting. She kept on shouting... I opened the window and I asked her 'Can I help you, can I call the police for you?'
"She said, 'My kids'."