The Russell Square knife attack in London, in which one woman died and five were injured, follows warnings that Islamic State may be targeting people with mental health problems to inspire them to carry out such incidents.
Police said they are keeping an open mind over the motive behind the attack in central London, and said terrorism was "one line of inquiry that we should explore".
The killing is currently being investigated by the Metropolitan Police's homicide team with the support of the force's counter-terrorism unit, but Scotland Yard said early indications suggested "mental health is a significant factor in this case".
It comes just days after a schizophrenic knifeman who tried to behead a Tube passenger during an Islamic State-inspired rampage was sent to Broadmoor high-security hospital to begin a life sentence.
Somali-born Muhiddin Mire, 30, targeted strangers at random in the ticket hall at Leytonstone Underground station in east London on December 5 last year.
He grabbed fellow passenger Lyle Zimmerman and attempted to murder the 56-year-old musician after they travelled on the same train from Stratford to Leytonstone, where Mire lived alone in Sansom Road.
He will serve a minimum of eight and a half years before being considered for parole.
But Mire could serve the entirety of his sentence at the psychiatric unit, which has housed some of the country's most notorious criminals.
Elsewhere, a suicide bomber who injured more than a dozen people when he blew himself up in Ansbach, Germany, last month was reported to have received psychiatric care, including for two attempts on his own life.
And claims emerged after the Nice lorry massacre that the attacker had undergone psychiatric treatment.
A report from Europol last month said recent academic research has shown that around 35% of the perpetrators of "lone actor attacks" which occurred between 2000 and 2015 suffered from some sort of mental health disorder.
A previous paper published by the EU law enforcement agency said a "significant proportion" of foreign fighters had been diagnosed with mental health problems before joining IS.
One estimate put the number at 20%, while another suggested it was even higher.
Senior counter-terrorism figures in the UK have raised concerns that IS is deliberately targeting propaganda at people with mental health problems to encourage them to carry out violence.
Scotland Yard Commander Dean Haydon said material is aimed at the vulnerable to inspire atrocities.
Speaking in June, he said: "If you look at some of the propaganda that's coming out of IS and Syria and elsewhere, part of their propaganda is specifically targeted in relation to the vulnerable.
"We're not just talking about mental health here, we're talking about vulnerable individuals within the community."
Earlier this year it emerged that psychologists were being deployed to work alongside counter-terrorism units.
Assistant Commissioner Mark Rowley, the UK's most senior counter-terrorism officer, previously described how authorities were seeing a "very different dynamic".
Last year he told MPs around a quarter of investigations involve "vulnerable" people, adding: "So you have young people dealing with mental health issues and other challenges."