The shooting happened at Phoenix Road, near Euston station in central London, at 2.30pm on Saturday Swedish time.
The incident took place near the church of Saint Aloysius in central London where a funeral was taking place.
The man is believed to have used a shotgun and opened fire on the funeral guests as they left the church.
Critical but stable
In the act, six people were injured, two of whom were minor girls, seven and twelve years old.
The 7-year-old girl seems to have received the most severe injuries of the six, the police state that she is being treated in hospital and that the situation is critical but stable.
The 12-year-old girl has been discharged from the hospital.
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The shooting is said to have occurred near a funeral in progress.
Photo: James Manning/PA via AP/TT