Jeremy Corbyn’s latest effort to draw a line under the antisemitism row that has rocked the Labour party has been overshadowed by the leftwing national executive committee member Christine Shawcroft’s claim that it had been “stirred up” to attack him.

Shawcroft, who stepped down as chair of Labour’s disputes panel on Wednesday after questioning the suspension of an alleged Holocaust denier, used a Facebook post on Friday to insist the issue was “being stirred up to attack Jeremy”.

Her comments came to light just as Corbyn issued a conciliatory Passover message, conceding the party must “do better” in tackling antisemitism.

Shawcroft resigned after an email emerged in which she questioned the suspension of the Peterborough council candidate Alan Bull.

Bull was accused of sharing on Facebook an article headlined “International Red Cross report confirms the Holocaust of 6m Jews is a hoax”, illustrated with a photograph of the gates of the Auschwitz concentration camp.

In a public Facebook post on Friday, Shawcroft said she had not seen the “appalling and abhorrent” article before emailing leftwing colleagues on Labour’s ruling national executive council (NEC) to support Bull. “As soon as I saw it I told the member that he should have antisemitism training,” she added.

The Facebook post from Christine Shawcroft. Photograph: Facebook

“This whole row is being stirred up to attack Jeremy, as we all know,” Shawcroft went on. “That someone who has spent his whole life fighting racism in all its forms should find himself being accused of not doing enough to counter it, absolutely beggars belief.”

Shawcroft stressed in her post that she was “not a Holocaust denier and would not support a Holocaust denier”. But by airing the claim that the antisemitism protests have been an attack on Corbyn she reignited one of the most serious concerns for Jewish groups. She subsequently removed the post.

Shawcroft herself was suspended from the party in 2015 after publicly defending the disgraced Tower Hamlets mayor Lutfur Rahman.

Almost 40 Labour MPs and peers signed a letter on Thursday night calling for Shawcroft to be removed from Labour’s NEC altogether – and other senior Labour figures on Friday added their voices to calls for her to step down, after her Facebook post emerged.

The Hackney mayor, Philip Glanville, tweeted: “Frankly jog on and don’t let the door hit you on the way out.” The Labour MP Jess Phillips said: “The idea that the whole thing is a conspiracy is part of the problem”, suggesting that Corbyn should personally urge Shawcroft to step down.

Richard Angell, of the centre-left campaign group Progress, said: “Holocaust deniers should be out of the Labour party and Christine Shawcroft should be too. The fact that she is still on the disputes panel is an insult.”

Shawcroft is due to leave the NEC in June when fresh elections will be held. If she resigned her seat now it would fall to the next most popular candidate at the last NEC election – the comedian and Corbyn critic Eddie Izzard.

The Labour leader’s office pressed her to give up the disputes panel chair on Wednesday but does not intend to intervene further.

Several NEC insiders have told the Guardian Bull’s case was not an isolated one, and Shawcroft and allies in the “left caucus” of the NEC regularly cast a sceptical eye over cases brought to the disputes panel – on which all NEC members sit – fearing them to be politically motivated.

Demonstrating that Labour has a firm grip on antisemitism will be one of the first and most pressing challenges facing its new general secretary, Jennie Formby, when she starts in the job next Tuesday, and she is expected to address the issue directly when she speaks to staff.

Corbyn’s office is in a standoff with Jewish leaders, who have demanded a meeting with him.

The Board of Deputies and Jewish Leadership Council, who organised Monday’s protest outside parliament, have set out a series of preconditions before they will sit down with him.

Corbyn’s team believes some of these are impossible to meet in the short term if at all – such as the appointment of an independent ombudsman to oversee antisemitism disciplinary cases, who would report to the Board of Deputies as well as to Labour.

In his message, Corbyn said: “Passover is a time to celebrate a journey from oppression to freedom. We remember all our Jewish brothers and sisters, who have battled against discrimination and faced the most horrific acts of violence and mass murder.”

Play Video 1:58 'We all need to do better': Jeremy Corbyn's Passover message to the Jewish community – video

He then highlighted rising antisemitism in Poland and France and added: “It is easy to denounce antisemitism when you see it in other countries, in other political movements. It is sometimes harder to see it when it is closer to home.

“We in the labour movement will never be complacent about antisemitism. We all need to do better. I am committed to ensuring the Labour party is a welcoming and secure place for Jewish people.

“And I hope this Passover will mark a move to stronger and closer relations between us and everyone in the Jewish community.”