He also claimed “globalists have wanted to have some form of conflict with Russia as an argument for us all to surrender our national sovereignty and give it up to a higher global level”.
Antisemitism watchdog the Community Security Trust said Mr Farage's language were "familiar code words for antisemitic conspiracy theories".
A CST spokesperson called Mr Jones “a notorious conspiracy theorist who should be beyond the pale for any mainstream politician”.
“Furthermore, for Jones’s conspiracy-minded audience, Farage’s references to ‘globalists’ and ‘new world order’ will be taken as familiar code words for antisemitic conspiracy theories,” they added.
A spokesman for the Board of Deputies said: “It is vital that our politicians distance themselves from conspiracy theories and conspiracy theorists, including those who trade in antisemitic tropes.
"We would call on Nigel Farage to repudiate these ideas and to commit not to dignify oddball nasties like Alex Jones with his presence again.”
Asked at Tuesday’s Brexit Party press conference about his appearances on Mr Jones’s Infowars how, Mr Farage said: "I've done a huge amount of global media, including Chinese state media.
"As far as the Infowars site is concerned I’ve done it every couple of years. I know Jones is accused of conspiracy theories & there may be some truth of that. I have never been a conspiracy theorist.”
On Sunday, it emerged two senior members of Mr Farage’s Brexit Party were still directors – despite supposedly resigning after offensive social media messages were exposed.
The Guardian reported ex-party leader Catherine Blaiklock, who resigned after calling Islam "incompatible with liberal democracy", and Michael McGough, who resigned after saying, among other things, that Ed and David Miliband and Peter Mandelson had “shallow UK roots”, were still listed as directors.
Ms Blaiklock also retweeted far-right messages, including a reference to "white genocie" by a former BNP activist.
