Brendan Cox warned Mr Farage was heading for a “slippery slope” after the right-wing politician linked the carnage in the German capital with Chancellor Angela Merkel’s policies.
Campaign group Hope Not Hate said it had asked the former Ukip leader to apologise for suggesting its supporters “masquerade as being lovely and peaceful but actually pursue violent and very undemocratic means” or face legal action.
Mr Farage’s comments on radio station LBC came after Brendan Cox had criticised a tweet sent by the right wing politician which linked the Berlin atrocity with Chancellor Angela Merkel’s policy on refugees.
In an appeal for funds on its website entitled “Help us take Nigel Farage to court”, Hope Not Hate said: “This morning, on LBC radio, former Ukip leader Nigel Farage launched an outrageous attack on us, on Brendan Cox, husband of murdered MP Jo Cox, and by association on everyone who believes in Hope not Hate.
“Our lawyer has just sent Farage a letter demanding he retracts and publicly apologises or we will begin legal proceedings against him.”
Early on Tuesday Mr Farage, who stood down as Ukip leader in November, took to social media in the wake of the outrage, which left at least 12 dead at a Christmas market, saying: “Terrible news from Berlin but no surprise. Events like these will be the Merkel legacy.”
The comment prompted hundreds of retweets and replies, including from Mr Cox, whose Labour MP wife was shot and stabbed to death by neo-Nazi Thomas Mair in her Batley and Spen constituency days before June’s EU referendum .
Mr Cox replied to the tweet by telling the politician that “blaming politicians for the actions of extremists” was a “slippery slope”.
Later, in an radio interview, Mr Farage responded by saying: “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.
“I’m sorry Mr Cox, it is time people started to take responsibility for what’s happened. Mrs Merkel had directly caused a whole number of social and terrorist problems in Germany, it’s about time we confronted that truth.”
This prompted angry replies from Mrs Cox’s former colleagues in Westminster.
Chris Bryant, the Rhondda MP and former shadow Commons leader, said: “The sheer nastiness of Farage sometimes takes my breath away.”
Chesterfield MP Toby Perkins added: “When your entire career has been built on hate, not hope, it perhaps shouldn’t shock me, but Farage still sinks lower than I’d have believed.”
Tracy Brabin, who won the by-election to succeed Mrs Cox in her Batley and Spen constituency, said: “Beggars belief... A new low for Farage.”
Mrs Merkel has shifted her policy on refugees and migrants to the right in recent weeks, including a speech in which she suggested stemming the number entering Germany and restricting the use of face veils.
Germany admitted almost 900,000 migrants in 2015 after deciding to allow in those who had made it to Hungary.
Although the numbers have dropped sharply this year, Mrs Merkel’s CDU party has suffered internal strife and a string of poor election results.
In a statement, Hope Not Hate described Mr Farage’s remarks as a “political smear”, adding: “Hope Not Hate is a well-respected, civil society organisation whose more than 200,000 supporters come from all political persuasions. They are united by a common desire to combat racism and to do so using lawful, peaceful means.
“That Nigel Farage made his remarks in the context of a discussion about Jo Cox, who was so brutally murdered earlier this year, makes them all the more poisonous and hateful.”
Hope Not Hate was one of three groups who shared the proceeds of the Jo Cox memorial fund, which raised more than £1 million in three days after she was killed in June. It was shared with the White Helmets in Syria and the Royal Voluntary Service.
Mair, who killed 41-year-old mother-of-two Mrs Cox as she arrived to hold a surgery in her constituency, was handed a whole life sentence in November. The 53-year-old shouted “Britain first” as he fired three shots at the Remain campaigner and stabbed her 15 times on the afternoon of June 16.
After Mair was jailed, Mr Cox said he had committed the “most incompetent and self-defeating” act of terrorism.