Mrs Cox's husband said his wife "believed in a better world and she fought for it every day of her life"
Labour MP Jo Cox has died after she was shot and stabbed on a street in her West Yorkshire constituency.
The 41-year-old politician, who was married with two young daughters aged three and five, was also kicked and left lying bleeding on the pavement in Birstall, near Leeds, an eyewitness said.
Another witness reported three shots, including one "round the head area".
The attack is believed to have taken place as Mrs Cox came out of the town's library, where she had been holding an advice surgery and meeting constituents.
Mrs Cox, who was elected as MP for the Batley and Spen seat in last year's general election, was taken to hospital in a critical condition but police later confirmed she had died.
Her husband, Brendan Cox, said his wife "believed in a better world and she fought for it every day of her life with an energy, and a zest for life".
He also urged people to "fight against the hatred that killed her. Hate doesn't have a creed, race or religion, it is poisonous".
Mr Cox had earlier tweeted a picture of the former senior Oxfam activist near Tower Bridge, close to where the family have a houseboat.
A 52-year-old man has been arrested in connection with the attack. He has been named locally as Tommy Mair, and police say they are not looking for anyone else.
A 77-year-old man suffered non-threatening injuries in a nearby attack, according to officers.
British Labour leader Jeremy Corbyn described Mrs Cox's death as an 'horrific murder':
The whole of the Labour family, and indeed the whole country, is in shock and grief at the horrific murder of Jo Cox pic.twitter.com/obic5pOCS3— Jeremy Corbyn MP (@jeremycorbyn) June 16, 2016
Politicians from Ireland and the UK have been extending the sympathies to the family of Mrs Cox, including Taoiseach Enda Kenny:
What an appalling tragedy. Jo Cox, a mother doing her public duty, her life taken away. My deepest sympathies to her family.— Enda Kenny (@EndaKennyTD) June 16, 2016
In a statement, President Higgins said: "As all of us sympathise with her family, including her young children, all of us who are committed to democratic politics must also acknowledge our being shocked, appalled and outraged at the attack on her.
"Giving public service, assisting others and sharing in discourse at times of divided opinion is a necessary part of democracy. To see a young parliamentarian killed in the course of her work is especially shocking.
"That she has died in that service makes a dreadful comment on our times. Her loss must not be in vain," he added.
Minister Charlie Flanagan said: "The circumstances of the attack on Ms Cox and her resulting death are truly shocking. I extend my sincere condolences to Jo’s husband, family and friends and colleagues in the Labour party."
Irish Labour leader Brendan Howlin said it was a "dreadful atrocity", which he condemned "in the strongest possible terms".
The EU referendum Remain and Leave campaigns suspended their activities for Thursday and Friday as a result of the attack.
David Cameron cancelled a pro-EU rally in Gibraltar, and Enda Kenny - who is in the UK - said he will not make any more comments on the campaign over the coming days.
Eyewitness Hichem Ben Abdallah said a "very brave" bystander tried to stop a man who pulled out a gun and shot her twice and also assaulted her.
Some reports said that two men had been involved in an argument in the street before Ms Cox intervened and was then attacked.
Mr Abdallah, who was in a cafe next door to the library, said he saw people rushing down the road towards the library and heard two shots.
He saw a man wearing a "dirty white baseball cap" who started "jostling with somebody", a bystander who appeared to be trying to stop him.
He said: "There was a guy who was being very brave and another guy with a white baseball cap who he was trying to control, and the man in the baseball cap suddenly pulled a gun from his bag.
"He was fighting with her and wrestling with her and then the gun went off twice."
He described a hysterical situation with lots of people screaming and said he was "absolutely shocked".
He added that the gunman walked off "very, very coolly, very slowly".