The announcement came as David Cameron and Jeremy Corbyn paid tribute to one of Parliament’s “most passionate and brilliant campaigners” on an emotional visit to the site where Mrs Cox died, in the town of Birstall, near Leeds.
Campaigning in the EU referendum remains suspended amid growing calls for the tragedy to put a halt to increasingly vitriolic political debate.
The Prime Minister issued a plea to drive intolerance “out of our politics and out of our public life”.
Labour leader Mr Corbyn said he had asked for Parliament to be recalled to enable politicians to pay tribute to Mrs Cox “on behalf of everybody in this country who values democracy … free from the kind of brutality that Jo suffered.”
Police last night confirmed they were looking into whether the man arrested for the killing, Tommy Mair, had links with far-right extremism after reports he had Nazi literature in his home. They are also examining his medical history amid reports he had mental health issues,
Mrs Cox, who won election last year to the Batley and Spen seat where she was born and raised, was shot and stabbed after holding a constituency advice surgery.
Flags were flown at half-mast at the Scottish Parliament, the Palace of Holyroodhouse, and at government buildings across Scotland and the UK yesterday as a mark of respect. Hundreds of people attended a vigil in Parliament Square in London last night, with public gatherings in memory of Mrs Cox, a mother of two, held in Edinburgh and Glasgow.
A motion of condolence was lodged at Holyrood by Scottish Labour leader Kezia Dugdale, calling on all political campaigners to “conduct our public debate with good humour, understanding and her enduring spirit to make the world a better place”.
It has emerged that parliamentary security authorities issued guidance to MPs in the wake of Mrs Cox’s death, urging them to consider ending open-door constituency advice surgeries, and opt for appointment-only meetings instead.
However, dozens of elected members insisted they would keep to their existing schedules in defiance of tragedy and grief. Nicola Sturgeon tweeted yesterday: “Politicians all over the country will hold surgeries today. We’ll do so with heavy hearts. But it’s what we do. May it never change.”
Laying flowers in the centre of Birstall, where an impromptu shrine has sprung up opposite the cordoned-off crime scene, Mr Corbyn called the killing “an attack on democracy” and described Mrs Cox as “an exceptional, wonderful, very talented woman”.
He added: “In her memory, we will not allow those people that spread hatred and poison to divide our society, we will strengthen our democracy, strengthen our free speech.”
He also praised the “wonderful” statement released by Brendan Cox in the hours after his wife’s death, which said that “in her memory we should try to conquer hatred with love and with respect”.
Standing alongside the Labour leader, Mr Cameron said: “If we truly want to honour Jo, then what we should do is recognise her values – service, community, tolerance – the values she lived by and worked by, those are the values that we need to redouble in our national life in the months and years to come.”
Parliamentary colleagues also made visits to the site of her fatal attack yesterday, many breaking down in tears. Hundreds of people of all faiths packed into nearby Saint Peter’s Church in Birstall for a service of remembrance .
Books of condolence were opened in the MP’s constituency and near the family’s houseboat home in London.
With news of Mrs Cox’s death reverberating across the world, German chancellor Angela Merkel issued her own plea for a more measured political debate, urging EU referendum campaigners to “draw limits” and warning that otherwise “radicalisation will become unstoppable”.
And Labour MP Yvette Cooper yesterday spoke out against the “very destructive” vitriol in EU referendum debate.
She said: “We don’t yet know the circumstances of this case but there has been an increase in vitriol, I think, in public debate. Some of that is directed towards MPs but some of it is people directing it at each other and that’s never healthy.”
She added that “there is more nastiness in public debate now and none of us would want to see that”.
In a harrowing account of Mrs Cox’s last moments, the father of the MP’s assistant, Fazila Aswat, described how his daughter tried to comfort her after the attack, cradling her as she lay bleeding.
Gulham Maniyar said of his daughter: “She tried to help her, she tried to hit the attacker with her handbag but he tried to go at her.
“She said her injury was so bad, and she was in her arms. There was lots of blood. She said, ‘Jo, get up’ but she said ‘No, my pain is too much, Fazila’. And I think those were the last words Jo spoke.”
Mr Mair, who is understood to have been born in Kilmarnock and moved to West Yorkshire as a child, remains in police custody.
In a statement, West Yorkshire Police said they had requested the assistance of anti-terrorism specialists, saying they were “aware of the inference of the suspect being linked to right-wing extremism”. The force’s temporary Chief Constable, Dee Collins, said officers were also examining the suspect’s links to mental health services.
In a statement released by the force, it emerged that a 77-year-old man who was injured during the attack had intervened to assist Mrs Cox.
He suffered a serious injury to his abdomen and remains in hospital in a stable condition.
A charitable fund set up in Mrs Cox’s name by friends had raised more than £100,000 last night, with the money going to causes championed by the MP. They include the Royal Voluntary Service, anti-extremism campaign Hope Not Hate, and the White Helmets, a volunteer search and rescue team operating in Syria.
The by-election to fill the Batley and Spen seat is likely to be uncontested, as the Conservatives, Liberal Democrats, Ukip and the Greens all said they would not put forward a candidate against Labour out of respect for Mrs Cox.