Officer Mike Pons of North Miami Beach Police says the alleged shooter was in a relationship with the mother of the children.
The two were arguing when the man allegedly started firing shots.
Both were dead when police arrived at the house late Saturday.
A 14-year-old girl and boys aged 13 and 10 were in critical condition Sunday at Jackson Memorial Hospital in Miami.
Another sibling, a 2-year-old boy, was unharmed and is in city custody.
The names of the victims have not been released.
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