Police in the UK have said possible far-right extremist links of the man suspected of killing Jo Cox are a "priority line of inquiry".
West Yorkshire Police temporary Chief Constable Dee Collins said the force is working with counter-terrorism officers to investigate the MP's murder - which they believe was a "targeted attack".
She said reports of suspect Tommy Mair's history of mental health problems are also a major line of inquiry as they try to establish why the popular Batley and Spen MP was shot and stabbed in her constituency on Thursday.
Ms Collins also revealed the Metropolitan Police had investigated two previous unrelated incidents in which the 41-year-old had received threats of a sexual nature at her Westminster office.
A 77-year-old man who "bravely" tried to save the MP as she was being attacked is in a stable condition in hospital after sustaining a serious abdomen injury, she added.
The update on the investigation came as hundreds of people attended vigils across the UK - including in Parliament Square, where a two-minute silence was held.
Speaking outside the Houses of Parliament, Mrs Cox's close friend, MP Wes Streeting, said: "The last 24 hours have felt like we are drowing in tears for our friend Jo."
Earlier, Ms Collins said: "Based on information available at this time, this appears to be an isolated, but targeted attack upon Jo - there is also no indication at this stage that anyone else was involved in the attack.
"However, we will be investigating how the suspect came to be in possession of an unlawfully held firearm."
She said Mr Mair had been medically examined and declared fit for detention and interview, while forensics experts were still examining his home, along with other scenes.
She confirmed Mr Mair was not an individual previously cautioned for sending malicious communications to Mrs Cox's Westminster office. The culprit in a second such incident has not been caught.
US civil rights group the Southern Poverty Law Center (SPLC) has also produced evidence that Mr Mair had links to American white separatist movement the National Alliance.
He was apparently sent an invoice for books with titles including "Incendiaries" and the "Improvised Munitions Handbook" - which includes instructions on how to make a handgun.
Witnesses described the weapon used by Mrs Cox's attacker - who is said to have shouted "Britain First" or "Put Britain First" as he shot and stabbed her - as looking home-made or like an antique gun.
Meanwhile, David Cameron and Jeremy Corbyn have come together in a show of unity to pay their respects to Labour MP Jo Cox.
