Mrs Cox's husband Brendan Cox released a statement saying that his wife would have wanted people to "unite" and to "fight against the hatred that killed her". People who go into public life, they want to act in the public interest, to pursue the national interest, to do things for other people, to make the country, make the world a better place.
Her death has sparked a debate over the safety of politicians, with the House of Commons re-issuing security guidance to MPs and telling them to call police if they have security concerns.
Six years ago, Mair was quoted in the local newspaper regarding his work as a volunteer at Oakwell Hall, a manor house popular with tourists in Birstall.
He said Mrs Cox was "an exceptional, wonderful, very talented woman, taken from us in her early 40s when she had so much to give and so much of her life ahead of her". There is no known link between Mair and the man behind the hate mail, the paper reported. "It's the well of hatred that killed her", the Labour Party leader said.
Cameron called for hatred, division and intolerance to be driven out of politics and public life, while Corbyn said that a "well of hatred" had killed the Labour MP.
USA 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 address on the receipts corresponded to Mair's address in a state housing project on the edge of Birstall, where two officers kept guard Friday as detectives interviewed neighbors.
Mair's brother Scott, 50, told The Sun tabloid that he was "struggling to believe what has happened".
Corbyn said: "We need our whole society to be secure". I don't even know who he votes for.
A man by the name of Thomas Mair from West Yorkshire also named as a former subscriber and supporter of the pro-Apartheid publication SA Patriot, according to the Associated Press.
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.
While no motive has yet been established for Cox's killing according to West Yorkshire police, Cox was a vocal supporter of immigration and remaining in the E.U. Her first speech in Parliament after she was elected described how beneficial immigration and ethnic diversity had been in Batley and Spen, her constituency.
The day before her killing, Cox joined her husband and two young children in campaigning for the pro-EU cause on the River Thames, where the family had lived in a houseboat since her election previous year.
Respects have been paid to mum-of-two Mrs Cox today, while both the Remain and Leave campaigns have suspended their campaigning with just six days until the European Union referendum.
Following a request from the Labour party, Cameron agreed to recall parliament from recess in order to honor Cox on Monday, announced Corbyn.
As police combed the sidewalks around the attack site Friday, some mothers walking their children to a nearby school wiped away tears. Others quietly spoke of the brutality of the killing and its exceptionally public nature.
Cox was a former aid worker who had championed the cause of Syrian refugees and campaigned for Britain to stay in the European Union when it votes in a referendum on Thursday. The first in her family to graduate from a university, she described her years at Cambridge as hard, telling the Yorkshire Post that is where she realized that "where you were born matters".