He said: "I recognise the offensive nature of my comments and that in diminishing the experiences of those who face antisemitism in our party and society I showed a lack of the sensitivity required for discussions around racism".
Jeremy Corbyn, leader of the United Kingdom's Labour Party, apologized for the "concerns and anxiety caused" after he participated in a 2010 event that compared Israel's actions in Gaza to the atrocities committed by the Nazis.
The recording's emergence comes amid a flare-up of a row over Jeremy Corbyn's handling of anti-Semitism by some members of the party.
He added: "I have no idea how he got himself into that situation but I am very pleased that he has apologised and on the back of that apology is the opportunity now to do something significant".
On Tuesday evening, Mr Willsman said he was "sorry" and "deeply regretted" his behaviour.
Well, you have to ask the question why they're in prison in the first place and since the releases that took place after the hunger strike I met numerous brothers including the brother who has been speaking here when they came out of prison when I was in Doha earlier this year, and you just realise that this mass imprisonment of Palestinians is actually part of a much bigger political game.
Labour said it did not comment on individual cases.
"One anti-Semite is one too many".More news: Donald Trump Takes Shot At LeBron James’ Intelligence In Wild Tweet
More news: Guardiola keen to learn from Sarri
More news: Amid bodyguard crisis, Macron loses ground in new poll
The Daily Mail reported that the Labour Party said Mr Corbyn's speech mentioning Leningrad and Stalingrad "was not comparing the actions of Nazis and Israelis but the conditions of civilian populations in besieged cities in wartime".
In the clip acquired by the Jewish Chronicle, Mr Willsman can be heard saying with a raised voice: "Some of these people in the Jewish community support Trump - they are Trump fanatics and all the rest of it".
"So I think we should ask the 70 rabbis, 'Where is your evidence of severe and widespread anti-Semitism in this party?'".
The alliance says it is anti-Semitic to accuse Jewish people of being more loyal to Israel than to their home countries, an example omitted from Labour's definition.
Marie van der Zyl, president of the Board of Deputies of British Jews, called Mr Willsman's outburst a "disgusting rant" against the Jewish community and rabbis, 68 of whom earlier this month complained of "severe and widespread" anti-Semitism within Labour ranks.
Jewish leaders have called for Labour to expel Mr Willsman and Labour MP Luciana Berger, parliamentary chair of the Jewish Labour Movement, told Sky News "anyone listening" to the audio of Mr Willsman's comments would be "appalled".
Speaking on Woman's Hour on BBC Radio 4, Dame Margaret said she had chosen to confront Mr Corbyn in anger at what she said was the party's "arrogance" over its new code of conduct on anti-Semitism.
The Labour leadership's reticence in adopting the IHRA definition and its examples has become a flashpoint in the row over anti-Semitism in the party.
The Chakrabarti report - which had already been published by the time of Mr Willsman's reported comments at the NEC - was condemned as a "whitewash" by critics.