Bidhya Sagar Das, 33, lived at the address in Finsbury Park area in north London where the toddlers were attacked in whatpolice are describing as a suspected "domestic incident".
"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," the Metropolitan Police said in a statement.
"The incident is believed to be domestic. There has been no arrest at this stage and enquiries continue," it added.
The boy was pronounced dead before 1:00 am after both the children were taken to an east London hospital.
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Police said next of kin are aware and a post-mortem will be carried out on the little boy in due course.
The little girl remains in a critical condition in hospital.
Officers were seen going door-to-door today as police remained outside the three-storey building. Neighbours said officers had been searching properties along the tree-lined street.
The Metropolitan Police have not confirmed how the children were injured, but said a murder investigation has been launched by its Homicide and Major Crime Command.