The Jeremy Corbyn-backing group Momentum has said anti-Semitism is “more widespread” within the Labour Party than was thought as it argued complaints cannot be dismissed “simply as right-wing smears”.

The grassroots group, which has played a key role in the Labour leader’s ascent, acknowledged the anger of Britain’s Jewish community at the “numerous” cases of anti-Semitism within Labour and the party’s failure to deal with them “in a sufficiently decisive, swift and transparent manner”.

In a significant intervention, Momentum’s National Coordinating Group (NCG) released a statement in which it revealed it had begun a process with external groups of developing anti-Semitism awareness training for Labour members.

Corbyn is facing demands to speed up the investigations into a backlog of around 70 complaints of anti-Semitism – including one against Ken Livingstone.

The Momentum statement follows a wave of left-wing comment on social media dismissing anti-Semitism complaints as smears from the Labour leader’s political opponents.

It statement stands in contrast to an open letter to Corbyn from a group called Labour Against The Witchhunt.

The letter – signed by more than 2,500 people including LAW chair Jackie Walker – blamed the allegations on “a cynical alliance between those who wish to deflect criticism of Israel and Zionism, and the right-wing in the Labour Party and the news media, who oppose your wider politics”.

The NCG, which agreed the Momentum statement, includes Christine Shawcroft, who quit Labour’s disputes panel and the party’s ruling National Executive Committee (NEC) amid criticism of her opposition to the suspension of a council candidate accused of Holocaust denial. The statement said:

“Accusations of antisemitism should not and cannot be dismissed simply as right-wing smears nor as the result of conspiracies.

“Current examples of anti-Semitism within the Labour Party are not only a problem of a few, extreme ‘bad apples’ but also of unconscious bias which manifests itself in varied, nuanced and subtle ways and is more widespread in the Labour Party than many of us had understood even a few months ago.”

While Corbyn’s opponents were “opportunistically using this issue as a way to undermine his leadership”, this did not reduce the need to challenge anti-Semitism, the statement said.

Meanwhile, Corbyn has vowed he would not tolerate any anti-Semitism in the party.

The Labour leader told Channel 4 News: “There is genuine concern and we are dealing with that concern… by investigating every case that is brought to our attention and if the person has committed an anti-Semitic act, in any way, then they are suspended and usually expelled from the party as a result of that.

“We are not tolerating anti-Semitism in any form in the Labour Party.”

The first task of new general secretary Jennie Formby when she takes up her role on Tuesday will be to appoint an in-house lawyer to ensure that procedures for dealing with allegations of anti-Semitism are “absolutely strong and watertight”, he said.

Corbyn said he was not aware of allegedly anti-Semitic social media posts made by a Labour candidate for local elections in Kent, Roy Smart, but that he was suspended as soon as they came to light.

The developments came as a Jewish member of Labour’s NEC, Rhea Wolfson, said she was frustrated at the pace of action on anti-Semitism.

Wolfson, who represents constituency Labour parties on the NEC, told BBC Radio 4’s Today programme: “There is very clearly a real issue, a huge piece of work that needs to be done in the Labour Party, around modern anti-Semitism and giving people the tools to recognise when legitimate criticism of Israel crosses the line into anti-Semitism.”

She added: “Action has been taken. I am frustrated by the pace of action, as I know a lot of people are – there is a heck of a lot more that needs to be done – but things have happened.”

Meanwhile, Eddie Izzard has called on the party to “stamp out the stain of anti-Semitism” that is being pushed by a “minority” of members as he replaces Shawcroft.

The comedian, actor and activist said Labour must “make amends and repair the damage with the Jewish community”, in line with the commitment given by Corbyn.