UK police investigating the murder of opposition MP Jo Cox have said the suspect's possible far-right links are a priority line of inquiry for detectives.

Cox, a 41-year-old mother of two, was shot dead on Thursday in the northern village of Birstall, near the city of Leeds.

The suspect, named by British media as local Thomas Mair, was arrested near the scene in connection with the killing of the Labour MP.

Police said counter-terrorism officers are also involved in the investigation into the attack which occurred as Cox arrived for a meeting with constituents.

West Yorkshire Police Temporary Chief Constable Dee Collins said police were also looking into the suspect's link to mental health services.

"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 enquiry which will help us establish the motive for the attack on Jo," Collins added in a statement.

Cameron and Corbyn came together to pay respects to Cox [Facundo Arrizabalaga/EPA] 

'It's the well of hatred that killed her'

The murder of Cox, a pro-EU advocate, has left Britain in shock and campaigning for the June 23 referendum on European Union membership has been suspended as a mark of respect.

Earlier on Friday, British Prime Minister David Cameron and opposition leader Jeremy Corbyn jointly paid tribute to the slain MP, and called for greater tolerance in public debate.

"Where we see hatred, where we find division, where we see intolerance, we must drive it out of our politics and out of our public life and out of our communities," Cameron said from Birstall, where he and Corbyn laid bouquets at the scene where Cox was shot.

With only a week until a referendum on whether Britain should leave the EU, which has split the country in two and sparked fiery debate on both sides, Cameron said it was time to "stand back".

READ MORE: Killing of MP Jo Cox halts Brexit campaigning in UK

Many commentators have questioned whether the killing could be linked to the referendum, which has stoked tensions by touching on issues of national identity and immigration.

"She was taken from us in an act of hatred, in a vile act that has killed her. It's an attack on democracy what happened yesterday. It's the well of hatred that killed her," Corbyn, the leader of the main opposition Labour Party, said.

 Jo Cox was known for campaigns for Syrian refugees [Stefan Wermuth/Reuters]

Cox, a former aid worker, was an advocate for Syrian refugees.

US advocacy group, the Southern Poverty Law Center, said that Mair, who had lived in Birstall for decades, was a "dedicated supporter" of National Alliance, once the primary neo-Nazi organisation in the United States.

The advocacy group said he had spent over $620 on reading material from the National Alliance, which advocated the creation of an all-white homeland and the eradication of Jewish people.

The group also said Mair had purchased a handbook with instructions on how to make a gun, noting that witnesses told British media the attacker used a gun which appeared "old-fashioned" or "home-made".

However, Al Jazeera's Barnaby Phillips, reporting from Birstall, said Mair's neighbours told him the suspect was a soft-mannered man who expressed no interest in politics.

"If there were any dark corners, they were extremely well-hidden," Phillips said. "He enjoyed his voluntary work teaching English to foreigners who settled in this area."

Source: Al Jazeera and agencies