Police are investigating possible links to right-wing extremism in their probe into the murder of Labour MP Jo Cox.
West Yorkshire Police said they are working with the North East Counter Terrorism Unit as the probe into the killing of the 41-year-old continues.
The mother-of-two was attacked in the street outside her constituency surgery in Birstall, near Leeds in West Yorkshire, at lunchtime on Thursday.
Tommy Mair, 52, was detained shortly after the attack and remains in police custody.
West Yorkshire Police said: "A murder investigation is under way by West Yorkshire Police who are working together with the North East Counter Terrorism Unit, who will bring specialist assets in support of the inquiry.
"We are aware of the speculation within the media in respect of the suspect's link to mental health services and this is a clear line of inquiry which we are pursuing.
"We are also aware of the inference within the media of the suspect being linked to right-wing extremism which is again a priority line of inquiry which will help us establish the motive for the attack on Jo."
Tributes have been paid to the mother-of-two, described by her party leader Jeremy Corbyn as someone who "stood for tolerance, justice, peace and human rights".
The attack on Cox is believed to have been "an isolated, but targeted" one, the force said, adding that they believe the person responsible was acting alone.
An eyewitness to the killing said he heard the attacker shout "put Britain first".
It has emerged a Thomas Mair has been named in a newsletter produced by a right-wing organisation which has called for a return to apartheid-style government in South Africa and been linked to the Neo-Nazi organisation National Alliance (NA) dating back to 1999.
Both the Remain and Vote Leave sides have suspended national campaigning in the light of the death of Cox, who entered Parliament in last year's general election.
In an apparent reference to the referendum campaign, German chancellor Angela Merkel urged British politicians to "draw limits" around the language used in political debate, warning that otherwise "radicalisation will become unstoppable".