The Met Police say Bilal Safi, six, Mohammed Ebrar Safi, five, and Mohammed Yaseen Safi, three, were taken from their foster home in Coulsdon on Thursday, August 20.
Scotland Yard said the youngsters were playing in the garden while their foster carer was in the house.
Specialist detectives are searching for their father Imran Safi, 26, who is said to have threatened their foster carer with a knife and used force to take the boys, who have not been seen since.
The force is also appealing for information regarding the whereabouts of a red Nissan Qashqai car, registration PK13 WFO, throughout last Thursday afternoon in the Croydon area.
Eight people have been arrested on suspicion of involvement in the abduction of the three boys.
This is a developing news story, more to follow.