The Labour MP, who was shot and stabbed after holding an advice session for her constituents in West Yorkshire, had campaigned for Britain to remain in the EU and championed the contribution of immigrants to British society.
She was also an active supporter of Syrian opposition groups against the country's President, Bashar al-Assad.
US politician Gabrielle Giffords, herself the victim of an assassination attempt at a political rally in 2011, wrote on Twitter that she was "absolutely sickened" by the killing, praising Mrs Cox as "young, courageous, and hardworking. A rising star, mother, and wife".
Ms Giffords survived being shot in the head in an attack that left six people dead and many injured. She was put in an induced coma and endured weeks of slow recovery.
US Secretary of State John Kerry said the killing was "an assault on everyone who cares about and has faith in democracy".
Germany's government tweeted about the "sad and terrible news of British MP Jo Cox", adding that "our thoughts are with her husband and children".
French Prime Minister Manuel Valls said on Twitter that the assassination was an attack on the democratic ideal and called on people to "never accept that!"
Spanish Prime Minster Mariano Rajoy said in a letter his British counterpart that "violence has no place in democracy" and asked Prime Minister David Cameron "to convey our deepest and sincere condolences to their families, relatives and all the British people".
Dutch Finance Minister Jeroen Dijsselbloem, who also chairs the group of eurozone finance ministers, tweeted that the UK was "a beacon of peaceful politics, I hope the people of the UK can make their democratic choices serenly and in safety next week".
Nato Secretary General Jens Stoltenberg  tweeted he was "saddened by the terrible murder" and included a statement from Mrs Cox's husband in his tweet.
Media in Europe and the US report the killing, stressing the role of Mrs Cox as a determined campaigner for Britain to remain in the European Union in the forthcoming referendum on 23 June.
The motive for the murder is still unclear but witnesses say the killer shouted "Put Britain first!" before repeatedly shooting and stabbing Mrs Cox.
Campaigning in the EU referendum has been temporarily suspended, with British politicians widely condemning the attack and expressing their condolences for the family.
Mrs Cox's role as a vocal supporter of Syrian opposition groups and refugee rights has also brought many expressions of solidarity and condolence.
The Syrian White Helmets non-partisan volunteer rescue group tweeted: "Our thoughts and prayers are with @Jo_Cox1 and her family."
The British MP had given a passionate speech on the crisis in the embattled Syrian city of Aleppo and was co-chair of a recently formed cross-party parliamentary group on Syria.
Syrian journalists in exile have also expressed their grief at the death of someone who they saw as a strong voice of support.
Before entering Parliament, Mrs Cox worked for a number of charities including Oxfam and the Bill & Melinda Gates Foundation.
Oxfam chief executive Mark Goldring tweeted that all at Oxfam were "devastated at the loss of our much loved and admired former colleague #Jo Cox MP".

The port at Invergordon is providing space for storing parts for the turbines and also office accommodation.
The Beatrice Offshore Windfarm Limited is being constructed in the Moray Firth at a cost of Â£2.6bn. Energy firm SSE is among the scheme's investors.
A total of 84 turbines are to be installed by Seaway Heavy Lifting.
The Nigg Energy Park, also on the Cromarty Firth, is also being used for the construction of the wind farm.
Fife-based Burntisland Fabrications Ltd (BiFab) is manufacturing offshore jacket substructures for the scheme at its yards in Arnish on the Isle of Lewis and Burntisland and Methil in Fife.

The former Scotland Under-21 international was released by Crystal Palace after he failed to make an appearance during his two years.
Kettings, 23, spent three months on loan at National League side Bromley last season, playing 14 times.
He is the sixth new signing since Northern Ireland assistant Stephen Robinson was appointed as manager.
Find all the latest football transfers on our dedicated page.
Tributes to British MP Jo Cox have poured in from politicians and public figures around the world.
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Port of Cromarty Firth has secured two contracts related to the construction of a massive offshore wind farm in the Outer Moray Firth.
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League One side Oldham Athletic have signed goalkeeper Chris Kettings on a one-year deal.