The Labour leader issued a Passover message to address his party’s anti-Semitism row, which has seen him come under increasing pressure this week.
Some 39 Labour MPs and peers have written to Mr Corbyn urging him to suspend a close ally from Labour’s ruling body.
The group wants Christine Shawcroft removed from the National Executive Committee (NEC) after she backed a local council candidate accused of anti-Semitic social media posts.
In a since deleted statement on Facebook, Ms Shawcroft claimed she had “not seen the appalling and abhorrent post” and wouldn’t have sent a supportive email if she had.
However, she also claimed the “whole row” over anti-Semitism is “being stirred up to attack” Mr Corbyn.
She later revised her statement to omit the reference to an attack on the Labour leader.
Naz Shah, although not among the Labour MPs to sign the letter to Mr Corbyn, said it was “right” Ms Shawcroft has resigned as the chair of Labour’s internal disputes panel.
Asked by Sky News if Ms Shawcroft should be suspended from the party, Ms Shah said: “It’s for the NEC to make those decisions but those decisions are being very, very closely watched across the country.
“The NEC has a duty to uphold our values and I have confidence that in this case they will do.”
She added Labour should be “the natural home for the Jewish community” and that it is “shameful” the party has not been “of late”.
Ms Shah was herself suspended by Labour in 2016 over comments she made about Israel, but was later reinstated after apologising and admitting her “ignorance” for the Facebook posts.
In his Passover message, Mr Corbyn described the holiday as “a time to celebrate a journey from oppression to freedom”.
In a video published on his social media channels, the Labour leader said: “We remember all our Jewish brothers and sisters, who have battled against discrimination and faced the most horrific acts of violence and mass murder.”
Mr Corbyn also spoke of anti-Semitism around the world, as he highlighted new Polish laws making it illegal to acknowledge the country’s complicity in the Holocaust, along with the rise of the National Front in France and the murder of a Holocaust survivor in Paris.
He added: “It is easy to denounce anti-Semitism 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 anti-Semitism. 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.
“In the fight against anti-Semitism, I am your ally and I always will be.”
In his two previous Passover messages as Labour leader, in 2016 and 2017, Mr Corbyn did not explicitly mention anti-Semitism.
Meanwhile, amid recent allegations that have put fresh pressure on Mr Corbyn this week, the Labour leader’s office has declined interviews with Sky News.
Mr Corbyn also failed to make an appearance at a scheduled event at a housing development on Thursday, where broadcasters had sent cameras.
On Monday, the Jewish Leadership Council (JLC) and the Board of Deputies for British Jews organised a demonstration outside Parliament against Mr Corbyn’s handling of anti-Semitism within Labour.
It came after Mr Corbyn apologised when it emerged he had questioned the removal of an anti-Semitic mural from east London in a Facebook post.
On Thursday, Labour peer and TV scientist Lord Winston claimed Mr Corbyn has “encouraged anti-Semites and he’s endorsed them”.
The Labour leader has offered an urgent meeting with the two groups and told Jewish leaders he is “sincerely sorry”.
They have demanded Mr Corbyn publicly condemn people vilifying those who protested outside Parliament, telling him they “are largely doing so in your name”.
They have also told the Labour leader it is essential any meeting leads to “concrete practical outcomes”.
Labour shadow chancellor John McDonnell condemned an open letter on Facebook, backed by more than 2,000 supporters of Mr Corbyn, that claimed Monday’s protest was “the full onslaught of a very powerful special interest group”.
Mr McDonnell posted on Twitter: “Describing Jewish people as a ‘very powerful special interest group’ is an anti-Semitic stereotype that undermines not supports Jeremy and his determination to unite our communities.
“Let’s all come together now, not divide.”
The Board of Deputies said Mr McDonnell was “right to speak out on this disgraceful letter”, but noted the critical replies to McMcDonnell’s tweet “only prove the problem”.
In his own Passover message, JLC chairman Jonathan Goldstein said he hoped the holiday “will be the point at which it once again becomes unacceptable to peddle and hold anti-Semitic views”.
He added: “The writing has been on the mural for some time.
“Jeremy Corbyn described himself as a ‘militant opponent of anti-Semitism’, and as an ‘ally’ in our fight.
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“If he truly means what he says, he will have no problem in agreeing to the entirely reasonable requests of what we want a meeting with him to achieve.
“Our fight needs to become his too.”