Hillary Clinton, the presumptive Democratic presidential nominee, led the tributes saying she was horrified by the “assassination” and calling Mrs Cox a “rising star”.
She referenced Mrs Cox’s maiden speech which celebrated the diversity of her constituency.
“It is cruel and terrible that her life was cut short by a violent act of political intolerance,” Mrs Clinton said.
“It is critical that the United States and Britain, two of the world’s oldest and greatest democracies, stand together against hatred and violence.
“This is how we must honour Jo Cox - by rejecting bigotry in all its forms, and instead embracing, as she always did, everything that binds us together.”
Canadian prime minister Justin Trudeau tweeted a message in French and English.
He wrote: “On behalf of our Parliament and all Canadians, I offer my deepest condolences to the family and colleagues of British MP Jo Cox.”
Ireland’s premier Enda Kenny announced that, in light of the suspension of campaigning by the Leave and Remain groups, he would not be speaking on the EU referendum as planned.
He also tweeted: “What an appalling tragedy. Jo Cox, a mother doing her public duty, her life taken away. My deepest sympathies to her family.”
The president of the European Council, Donald Tusk, offered his condolences after a visit to Finland.
He said on Twitter: “Repelled by tragic attack on British MP Jo Cox. My thoughts are with her family and loved ones.”
Australian prime minister Malcolm Turnbull said he was “deeply shocked”.
He added on Twitter: “Our condolences, prayers and solidarity are with her family & the people of the UK.”
The Twitter account of the Malala Fund, the organisation led by Pakistani girls’ rights activist Malala Yousafzai, who survived being shot in the head by terrorists, retweeted a comment from her father.
Ziauddin Yousafzai tweeted a link to Mrs Cox’s speech calling on Britain to help the victims of the war in Syria and said: “May her soul rest in peace. Jo Cox left behind a legacy of love,respect &peace.”
US secretary of state John Kerry and Danish prime minister Lars Lokke Rasmussen also offered condolences to Mrs Cox’s friends and family.
Mr Kerry, who was travelling in northern Europe on Thursday, said the attack was “an assault on everybody who cares about and has faith in democracy”.
Mr Rasmussen called the killing “a true shock”.