The audio clip, leaked by website Guido Fawkes on Tuesday, appears to capture the former MP for Hyndburn repeatedly referring to “f***ing Israel”, at the Lancashire Labour Party meeting that led to the withdrawal of support for Rochdale candidate Azhar Ali.
Mr Jones lost his seat in 2019, but is hoping to stand again.
Mr Jones has now been suspended by Labour following the leak, it was understood on Tuesday evening.Labour would have to follow a formal process if the party wanted to strip him of his candidacy, but he is believed to have been called for an interview with party chiefs on Tuesday evening.
It is the latest row to emerge from the meeting of the Lancashire Labour Party, at which Rochdale by-election candidate Mr Ali was recorded suggesting that Israel had allowed the October 7 Hamas slaughter of more than 1,200 citizens as a pretext to invade Gaza.
Labour initially stuck by Mr Ali despite the deeply controversial remarks, before eventually cutting him adrift on Monday evening “following new information about further comments”.
Mr Ali, who has apologised, is now understood to have been suspended from the party pending an investigation.
But the delay in withdrawing support has led to widespread criticism for Labour leader Sir Keir Starmer.
Speaking as he campaigned in Wellingborough, Sir Keir said: “Certain information came to light over the weekend in relation to the candidate. There was a fulsome apology. Further information came to light yesterday calling for decisive action, so I took decisive action.
“It is a huge thing to withdraw support for a Labour candidate during the course of a by-election.
“It’s a tough decision, a necessary decision, but when I say the Labour Party has changed under my leadership I mean it.”
Sir Keir has sought to move his party on from the Jeremy Corbyn era, which was overshadowed by controversies over antisemitism.
But the party leadership is now being pressed on why Mr Ali had not been immediately suspended after the comments emerged.
Labour’s handling of the row was branded “shambolic” by the lawyer who led a review into the party’s culture, as the Conservatives also seized on the controversy.
Martin Forde KC said MPs within the party feel there has been a “disparity in treatment” of allegations of antisemitism.
Labour withdrew backing for Mr Ali after the Daily Mail reported that he had blamed “people in the media from certain Jewish quarters” for fuelling criticism of a pro-Palestinian MP.
Left-wing critics of the Starmer leadership accused him of showing inconsistency in the handling of the allegations.
The party recently suspended the MP Kate Osamor after she appeared to say the Gaza war should be remembered as genocide on Holocaust Memorial Day, for which she later apologised.
Veteran MP Diane Abbott also had the whip withdrawn immediately after suggesting Jewish, Irish and Traveller people are not subject to racism “all their lives” in a letter to the Observer last year.
She apologised and suggested “errors arose” in the drafting of the letter.
Mr Forde also highlighted the previous cases, saying “things seemed to drag on in terms of disciplining certain elements of the party, and be dealt with swiftly in others”.
Sir Keir on Tuesday denied that factionalism played a role in the handling of complaints or allegations of antisemitism.
“I set out four years ago to tear antisemitism out of the Labour Party. It’s the first thing I said I’d do as Labour leader, and to change our party.
“I have taken a series of decisions along those lines, ruthlessly changing our party, and it’s made no difference to me where somebody stands in the Labour Party.
“The change I’ve brought about is a Labour Party that is now back in the service of working people,” he told broadcasters.
He also said any allegations against other Labour councillors present at the event at which Mr Ali made his widely condemned remarks would be “fully investigated by the party”.
A spokesperson for Campaign Against Antisemitism said the latest comments attributed to Mr Jones “are not only ignorant but grossly offensive”.
“Labour must make clear that it will not back Graham Jones’ rhetoric and his candidacy.”
Labour’s decision will add considerable uncertainty to the outcome of the Rochdale by-election when voters go to the polls at the end of the month.
Also running in Rochdale are former Labour MP Simon Danczuk, now the Reform Party candidate, and George Galloway, of the Workers Party of Britain, who is campaigning against Labour’s stance on Gaza.
About 20% of the electorate and 30% of the population of the town are Asian, with polls nationally suggesting Labour’s vote could be hit by Asian people unhappy with the party over Palestine and its perceived support for Israel.
If elected, Mr Ali will sit as an independent MP and will not receive the party whip.
The decision means that Labour will also need to find a new candidate to contest the seat at the upcoming general election.
The Tories sought to pile further pressure on Sir Keir over the row, even after the decision to ditch Mr Ali as a candidate.
Defence Secretary Grant Shapps said: “Sir Keir Starmer says he’s taken tough and decisive action over Labour’s candidate in Rochdale.
“But the truth is that this shouldn’t be tough – it should be the simplest thing to do the right thing and stand up against antisemitism.
“And it clearly is not decisive because Labour have been backing their man throughout this and have only done yet another U-turn because of the headlines.
“How can the public, and particularly the Jewish community, have any trust in Labour when Keir Starmer seems to be protecting those who heard what was said and did nothing.”