"Police are working with our partner agencies to ensure that support is wrapped around those most directly affected by the tragic events of last night, and the wider community and we urge anyone who needs support to reach out."
Police would not be drawn on who found the dead children.
Canterbury District Commander Superintendent John Price said whenever police faced a tragedy like this it was hard.
"A lot of us are parents," he said.
But he assured his investigation team were professional and determined to do their best for the victims.
Price would not say more about the family, including whether either parent of the dead children were working.
He said it was "unfortunate" that there had been two tragedies in Timaru in such a short time.
He could not say when the names of the children would be released.
"We have to notify next of kin and you can appreciate that will take some time... my understanding is their next of kin are overseas in multiple countries."
He said the family had a network of friends in New Zealand but no family.
Deputy PM Grant Robertson has also spoken about the incident.
It's a tragic event and will be distressing for the people of Timaru and the family, Robertson said, and his heart goes out to the community.
Detectives launched a homicide investigation after the children were found dead at a residential address overnight.
The Otago Daily Times understands the woman in hospital is a suspect in the deaths.
A hospital staffer told the Herald that while everyone was discussing what happened no one knew who was involved or the details.
They said a number of specialists and surgeons from overseas lived in the Queen St houses where the deaths took place but he did not know who was occupying them currently.
Detective Inspector Scott Anderson said emergency services were called to the address shortly after 10pm last night.
"On arrival at the scene, emergency services found three deceased people. One other person has been hospitalised," Anderson said in a statement.
Jade Whaley lives next door to where the incident took place and said that at about 9.40pm last night she and her husband heard banging, followed by sobbing and moaning.
Police officers are going door to door speaking to neighbours.
"We went outside and realised it was coming from the neighbouring property."
There are three units on one side of the Whaleys' property and while outside they saw a fellow neighbour speaking to a person at the back unit.
Timaru Mayor Nigel Bowen said the community will be devastated by the tragedy.
"Again, unfortunately. It seems that the community has had layers of tragedy with the five young lads that passed away so it's really tough," he said.
He said the area where the incident took place is "just a typical suburb" and relatively quiet.
"I think the community will be thinking, why is it happening to a place like ours?
"There's a lot of pressures on society at the moment, you have to question the support around mental health, are we doing things right in this country? I question that we're probably not."
WHERE TO GET HELP:
If you are worried about your or someone else's mental health, the best place to get help is your GP or local mental health provider. However, if you or someone else is in danger or endangering others, call police immediately on 111.