If the petition gets 100,000 signatures before the 23 June poll it would normally trigger a debate.
Jo Cox's family say she will always 'live on through all the good people in the world'.
Bernard Kenny, 77, was stabbed in the abdomen by a gunman who killed the MP for Batley and Spen.
The 52-year-old was remanded in custody during an appearance at Westminster Magistrates Court.
Donations will be distributed to three charities that were 'close to her heart'.
Obama offers his condolences on behalf of American people after 'heinous' murder, the White House said.
Some have said Mair shouted 'Britain First' during the attack, a possible reference to the far-right group.
Lord Kinnock said he and wife Glenys are left grief-stricken by the brutal murder of MP Jo Cox.
Jo Cox killing: GoFundMe fundraising page for charities chosen by MP's family raises £100,000 in 5 hours
The MP for Batley and Spen was shot and stabbed on 16 June outside her constituency surgery in West Yorkshire.
Race hate of MP-killer suspect revealed as officers discover Nazi insignia during search of home.
Father of assistant to MP for Batley and Spen describes how his daughter comforted the dying MP.
'She is irreplaceable,' said one member of the community.
She fought tirelessly for democratic politics as the way to change the world for the better.
Jeremy Corbyn, David Cameron and John Bercow have all backed the 20 June move.
Neighbours describe Mair as a caring and solitary man who helped others, often working as a volunteer.
Thousands take time to thank local politician following shooting of MP for Batley and Spen.
A vote will be held for the West Yorkshire constituency Batley and Spen in the future.
MP and friend of late Labour politician gives an emotional statement to the Canadian House of Commons.
Mourners speak to IBTimes UK near to the House of Commons after Jo Cox's killing.
Tributes are pouring in for the Labour MP after she was killed by a man wielding a gun and knife.
Authorities have urged politicians to contact their local police force if they have any concerns.
Tributes have poured in for the late Labour MP who was attacked in her West Yorkshire constituency.
Hillary Clinton urges US and Britain to "stand together against hate and violence."
MP had been giving a weekly advice surgery in her Batley and Spen constituency.
Police investigate background of suspect in killing of Labour MP.
Husband of the murdered Labour MP promised to 'fight against the hate' that killed his wife.
Labour MP Jo Cox was shot dead in her constituency in West Yorkshire.
MP has died after she was shot and stabbed by man in her constituency near Leeds.
Jo Cox: MP was rising Labour star when she was killed in shooting and stabbing attack near her Leeds constituency
A West Yorkshire Police spokesman said a 52-year-old man has been arrested in connection with the killing.
The 41-year-old was seen lying and bleeding on the pavement in Birstall, West Yorkshire.