The mother of a backpacker slain in an Australian hostel wrote an open letter to US President Donald Trump, rejecting the decision to label her daughter's death as a "terror attack."

The slayings of Mia Ayliffe-Chung, 20, and fellow Brit Tom Jackson, 30, were on a list of 78 attacks the White House says were "executed or inspired by" the Islamic State terror group - and under-reported by the media.

Rosie Ayliffe says the possibility of terrorism was discounted early in the investigation.

"My daughter's death will not be used to further this insane persecution of innocent people," she wrote.

"This vilification of whole nation states and their people based on religion is a terrifying reminder of the horror that can ensue when we allow ourselves to be led by ignorant people into darkness and hatred."

Australian police allege that the suspect, Smail Ayad, of France shouted "Allahu akbar" - an Arabic phrase meaning during the attack, but said there was no indication the assault was motivated by extremism.

They have said they are investigating whether Ayad had a romantic obsession with Ayliffe-Chung.

The attack took place in front of dozens of backpackers at a hostel in northern Queensland.

Ayliffe-Chung was found dead at the scene. Jackson tried to stop the attack and was fatally wounded.

On Monday President Trump accused the media of deliberately minimising reporting of terrorist attacks, including high-profile Australian incidents.

"You've seen what happened in Paris and Nice. All over Europe it's happening. It's gotten to a point where it's not even being reported," Trump told a group of military leaders and troops.

"And in many cases, the very, very dishonest press doesn't want to report it. They have their reasons and you understand that."

The incident that involved the death of Ayliffe-Chung was on the list as were Man Haron-Monis' 2014 attack on Sydney's Lindt Cafe - in which two people died - and the fatal shooting of police worker Curtis Cheng in Parramatta 2015.

The list appeared to be hastily assembled, including several misspellings of the word "attacker."