Police revealed the girl remains in a serious condition and the boy is in a critical condition.
Both were taken to Dunedin Hospital with gunshot wounds after the incident in Invercargill about 1am today.
This evening, Southland Area Commander Inspector Mike Bowman said: "while the police investigation is in its early stages, this is almost certainly an isolated occurrence.
"We want to reassure the community that this appears to be a targeted attack.
"Our team is working hard to establish what has happened, and our priority is to identify those responsible as soon as we can and hold them to account."
A scene examination is continuing and police inquiries are ongoing.
Victim Support is working with members of the victims' families
Police were called to an Invercargill address shortly after the gunshots were fired.
Neighbours spoken to by the Otago Daily Times said the event was not totally unexpected as activity at the property had been becoming increasingly hostile and volatile in the past three or four weeks.
One neighbour said they had become more concerned over time because the escalating hostility coming from the rental property was impacting on the tight-knit and peaceful neighbourhood.
One person had witnessed two people being loaded into the back of a ute vehicle which then drove off quickly in the direction of Southland Hospital shortly after the gunshots were heard.
Neighboors were unsure what may have caused the situation to escalate as there was no indication or noticeable event, nor any cars coming or leaving prior to the shooting, which may have indicated trouble brewing.
