Cameron and Corbyn made a rare joint visit to the scene of the crime - the village of Birstall - to pay their tributes to 41-year-old Cox, who had been campaigning for the UK's continued membership of the 28-member European Union (EU).
Cameron described Cox as a "passionate and brilliant" member of Parliament who died doing her job and Corbyn announced that Parliament, which had gone on recess, will be recalled on Monday so that MPs can pay their respects to Cox.
"Jo died doing her public duty at the heart of our democracy, listening to and representing the people she was elected to serve," Corbyn added.
Vote Leave and Remain have both suspended campaigning for next Thursday's EU referendum in light of the attack.
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The entire British political establishment was reeling from shock as Cox's opening speech to Parliament was replayed on television, in which she celebrated her Indian-origin and other immigrant constituents of Batley and Spen.
"Our communities have been deeply enhanced by immigration, be it of Irish Catholics across the constituency or of Muslims from Gujarat in India or from Pakistan, principally from Kashmir.
"While we celebrate our diversity, what surprises me time and time again as I travel around the constituency is that we are far more united and have far more in common with each other than things that divide us."
It emerged today that Cox had received a stream of threats over three months but had not been provided with any extra security.
Downing Street sent additional safety guidance to other MPs after yesterday's attack on Cox outside a library in the town she grew up in.
Witnesses say Cox was shot a third time in the face and
the suspect was trying to reload his antique-style weapon when another man tackled him.
The man suffered minor injuries and the suspect, who is said to have lunged at others who attempted to intervene, walked away from the scene shortly before being arrested.
The SPLC published receipts that appear to show Mair bought, among other books, a manual on how to make a homemade pistol from the National Alliance.
Some eyewitnesses have claimed that Mair shouted "Britain first" during the attack on Cox, triggering speculation that he may have been a member of the far-right political group Britain First.
However, the group has denied any involvement, saying it "would never encourage behaviour of this sort."
West Yorkshire's Police and Crime Commissioner, Mark Burns Williamson, said: "I have worked closely with Jo since she was elected and I am deeply shocked that such a talented young woman has been senselessly attacked and killed whilst working in her constituency and serving her community.
"This is a truly shocking incident but I want to reassure communities that our information is that this is a localised incident, albeit one that has a much wider impact.
"I must stress that investigations are ongoing, a man has been arrested, and we need to let the police do their job in understanding exactly what has happened that led up to this hugely tragic incident and channel all our thoughts into supporting the families and communities affected."
"Jo would have no regrets about her life, she lived every day of it to the full. Jo believed in a better world and she fought for it every day of her life with an energy and a zest for life that would exhaust most people," her husband Brendan Cox said in a statement.
Buckingham Palace has announced that Queen Elizabeth II will write a private letter to the widower.
Vigils have been planned today and over the weekend in memory of the politician across the UK.