"We're looking at anybody that's had any involvement.
Everybody who's had any involvement at all in the past two or three days is a person of interest.
"We're not talking about naming suspects or identifying particular suspects at this stage."
He could not give a cause of death and the coroner and local pathologist were investigating.
Formal identifications of the children are yet to be made.
A woman, 34, was injured in the incident in the suburb of Manoora, 10 minutes from the city centre. She is in a stable condition in hospital and assisting detectives with their inquiries, police said.
Cairns is a tropical city with a population of more than 150,000 people and is popular with international tourists as a gateway to the Great Barrier Reef, one of Australia's biggest tourist sites.
Woman's cousin: 'I just can't believe it'
The Australian Associated Press cited the injured woman's cousin, Lisa Thaiday, as saying the children were all siblings and the woman was their mother.
It said another sibling, a 20-year-old man, arrived home to find his brothers and sisters dead inside the house.
A police block at an address in Manoora near Cairns where children have been stabbed to death. Photo / AAP
"I just can't believe it. We just found out (about) those poor babies," Thaiday said.
Reports widely said the children had been stabbed while the Cairns Post reported they were also suffocated, although police did not immediately confirm this.
Sky News, whose news anchor broke down in tears as the story was breaking, said a stepfather was known to live at the house, but his whereabouts were unknown.
Community reeling
Who killed the children remains unclear with Mr Asnicar saying there was no need for the public to be worried, suggesting no one was on the loose.
"As it stands there's no need for the public to be concerned about this other than the fact that this is a tragic, tragic event," he told a media conference.
"The situation is well controlled at the moment. There shouldn't be any concern for anyone else out of this environment."
He added that it was too early to know the chain of events.
"We need to do a lot more work as you can imagine," he said.
"The crime scene is being locked down and that includes from me. Nobody goes in there until our forensic people have finished and until we have done that we're not going to be able to clearly establish any relationships."
Cairns Post reporter Scott Forbes, who is on the scene, said the area where the bodies were found has a large indigenous population.
"All of the people here are actually related to the people who were involved in this incident," he told the Australian Broadcasting Corporation of those who live on the same street.
"So they're all reeling at the moment. But telling us that she was a very, very protective, very proud mother who loved her children dearly."
A couple who live around the corner said they did not feel safe in the area and it was not uncommon to hear fighting and drinking at night.
"It's pretty scary. Oh my God," the man, who did not want to be named, told reporters.
Abbott: 'These are trying days for our country'
"The news out of Cairns is heartbreaking," Prime Minister Tony Abbott said in a statement.
"All parents would feel a gut-wrenching sadness at what has happened. This is an unspeakable crime. These are trying days for our country."
The tragedy came a day after a Melbourne man, Charles Amon Mihayo, was jailed for life for smothering to death his two daughters, aged three and four, in a move the judge said was aimed at punishing his ex-wife.
And it follows hard on a dramatic siege in Sydney in which two hostages and a gunman were killed in an incident that sparked an outpouring of grief in Australia.
- AFP, AAP
