Police say they are looking into whether a French man who allegedly said "Allahu akbar" as he stabbed a 21-year-old British woman to death in a north Queensland backpackers' hostel has any links to extremist groups.

Key points: English woman Mia Ayliffe-Chung stabbed to death at north Queensland backpackers

English woman Mia Ayliffe-Chung stabbed to death at north Queensland backpackers British man, 31, critically injured in what was an attack in front of 30 people

British man, 31, critically injured in what was an attack in front of 30 people Frenchman who lived at hostel in custody allegedly said "Allahu akbar" before attack

Mia Ayliffe-Chung was stabbed to death and a 30-year-old man was critically injured in front of about 30 people at Shelley's Backpackers in Home Hill, south of Townsville, after 11:00pm on Tuesday.

A dog from the hostel was also killed.

A 29-year-old Frenchman who was living with the victims at the hostel is in custody, but has not been charged.

He used the Arabic phrase "Allahu akbar" both during the attack and his arrest, Queensland Police Service Deputy Commissioner Steve Gollschewski said.

"While this information will be factored into the investigation we are not ruling out any motivations at this stage, whether they be political or criminal," he said.

"We're working closely with our partner agencies to make sure if there is any indication that it has an extremist slant, or this person had been radicalised, we can discover that.

Sorry, this video has expired Police investigate possible 'extremist nature' of stabbing

"Investigators will also consider whether mental health or drug misuse factors are involved in this incident."

Deputy Commissioner Gollschewski said there were no ties to the Islamic State group and the attacker appeared to have acted alone.

The Frenchman has been in the country for about a year on a temporary visa and had no known local connections.

AFP Commander Sharon Cowden said he was lawfully in Australia and not known to any authorities.

The British High Commissioner has landed in Townsville and was due to hold briefings with authorities.

'Happy-go-lucky' Ayliffe-Chung 'dearly missed'

Ms Ayliffe-Chung had been working at a Gold Coast nightclub as a waitress before her adventures led her to a north Queensland cane farm for work.

"Day four done, just 85 left!" she wrote in one of her last Facebook posts.

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"Skills achieved; the ability to tell the difference between a rock and a clump of mud and throwing stones really far. The sun is too hot. Stupid Australia."

Owner of The Bedroom Lounge and Bar, Maxwell Pickering, verged on tears when speaking of Ms Ayliffe-Chung.

He said she became close with the team quickly, and they were going to try to have her back after a three-month stint on the farm.

"She was a beautiful person, fun, outgoing, and had an infectious ability to make everyone happy," Mr Pickering said.

"It's not a cliché what I'm saying, nobody had a bad word to say about her. She never had a problem, we loved having her around."

Her friends have expressed their grief on social media, describing her as a happy-go-lucky character who will be missed dearly.

"Today the world has lost one of the most beautiful young women to ever walk this planet," one friend wrote on Facebook.

Ms Ayliffe-Chung had been working at a cane farm in the days before her death. ( Facebook )

'We heard the screams'

A man who lives across the road, Ray, said he heard "blood-curdling screams" late on Tuesday night.

"It's a very quiet town ... we heard the screams ... I was terrified, it wasn't very pleasant at all. I'll never forget it.

"A sleepy little town like this, you don't expect things like that to happen.

"I'll never forget the screaming — I've never heard that before in my life. It's terrible."

Burdekin Shire Mayor Lyn McLaughlin extended sympathies to the families affected, adding the council would fly its flag at half mast on Wednesday.

"This is a tragic and very sad incident to have occurred in our small, peaceful and safe community," she said.

Caution urged over 'associating phrase with terrorism'

Police said it was believed the suspect was acting alone. ( ABC News )

The Islamic Council of Queensland's Ali Kadri was critical of the speculation so early on that the alleged attack could be linked to terrorism.

He said overplaying it was disingenuous and wrong.

"Media should be more responsible than this, and not just make it a terrorist incident because at this stage I don't think we can speculate it is a terrorist incident," he said.

"Just because someone says 'Allahu akbar' does not mean that person's motivations are religious.

"When Muslim women give birth they say 'Allahu akbar' does that mean the act of giving birth is terrorism?

"It is a commonly used phrase by 1.6 billion Muslims in the world, and unfortunately some criminals misuse that phrase.

"I think we should be cautious by not associating this phrase with terrorism and empowering the terrorists."

Meanwhile, federal MP Bob Katter held a press conference in response to the stabbing, saying he would call for tougher restrictions on migration at the next sitting of Parliament.

"The people that live between Greece and India and Northern Africa we cannot allow them to come into Australia unless they are persecuted minority groups, which obviously are the Christians the Jews and the Sikhs," he said.

"Now unless they fit into those categories, I think migration from those countries has to stop."