Nigel Farage has withdrawn a claim that a campaign group pursued "violent and undemocratic means" before the start of a libel case over the comments.
Hope Not Hate began legal proceedings over the comments made by Mr Farage on LBC radio last year.
It said it was "delighted" the ex-UKIP leader had withdrawn the claim.
However, Mr Farage said that while he accepted the group did not use violence, some people claiming to support it had behaved violently.
He denied it was a "victory" for the group, saying: "Despite them demanding up to £100,000 in damages I have not paid them a penny; they demanded an apology which I have not given and they demanded an undertaking to the court which they did not get."
Mr Farage sparked outrage among Labour politicians in December last year after linking the widower of murdered MP Jo Cox to "extremists".
He criticised Brendan Cox after he questioned the politician's claim that the Berlin lorry terror attack was "Merkel's legacy".
Mr Cox said "blaming politicians for the actions of extremists" was a "slippery slope".
Hours after the Twitter exchange between the two, Mr Farage went on LBC radio and said: "Well, of course, he would know more about extremists than me, Mr Cox, he backs organisations like Hope Not Hate, who masquerade as being lovely and peaceful but actually pursue violent and very undemocratic means."
Hope Not Hate said more than 16,000 people had donated to an appeal to fund libel action against Mr Farage.
The group's chief executive Nick Lowles said: "For too long right-wing politicians have got away with smearing and abusing their opponents. We drew a line in the sand and 'no more'."
Hope Not Hate said its supporters were not violent and were not involved in any incidents Mr Farage alleged took place against him.