Mr Cox said he hoped something positive could come of his wife's passing and added Jo would have wanted people to stand up for the principles she fought for "in her death as she did in life".
The former MP for Batley and Spen was described by her widower as having had "energy" and "a joy about life".
Jo, who would have been 42 tomorrow, "just wanted to make the world a better place, to contribute", Mr Cox added.
"I don't want people ascribing views to her she didn't have but I certainly want to continue to fight for the legacy and for the politics and the views she espoused," he said.
In a pool interview for TV broadcasters Mr Cox also thanked the public for their "incredible" response, commenting that they had helped his children to understand and deal with the loss of their mother.
"What the public support and outpouring of love around this does is it also helps the children see that what they’re seeing is what other people are feeling, that the grief that they feel isn't abnormal" he said.
"That they feel it more acutely and more painfully and personally, but that actually their mother was someone who was loved by lots of people and therefore it's okay for them to cry and be upset about it."
Mr Cox went on to claim his late wife, an ardent Remain campaigner and advocate of refugees' rights, had become worried about the tone of the EU referendum.
"She completely respected that people could disagree for very good reason," he said. "But more about the tone of whipping up fears and whipping up hatred potentially."
"I think the EU referendum has created a more heightened environment for it but actually it also pre-existed that. It's something that's happened over the last few years I think and again not just in the UK but globally."
Jo Cox was killed after being shot and stabbed outside a constituency surgery she was due to attend on Thursday last week.
A man, Thomas Mair, 52, has been arrested in connection with the killing and has appeared before a court charged with murder.