The shadow justice minister has spent more than nine years representing the Ashfield constituency but told local members that she did not know if she could give them “the commitment you deserve for what could be a further eight years”.
In comments carried on her website, the MP said a “lack of tolerance for different viewpoints in the Labour Party frankly worries me”.
“We have to have respect for each other, even if we disagree, because we are all part of this party,” she added.
“This party is about a set of values not any individual and we would all do well to remember that.
“And while I’m at it, and it doesn’t happen in Ashfield, but when I hear people being called right-wing in the Labour Party I find it utterly offensive.
“We are all left-wingers in this party – that is why we joined the Labour Party,” she said.
A letter from the body to shadow cabinet members called on them to address the issue and clarify their positions, stating: “The Labour Party currently attracts anti-Semites and repels Jews.
“This is a sickening situation for you and for us.
“But it is the undeniable truth.”
Labour MP Louise Ellman backed the call, tweeting: “It is time Jeremy Corbyn acted on Labour’s anti-Semitism crisis.”
The Board of Deputies of British Jews has also written to the shadow cabinet outlining action they want taken to combat anti-Semitism.
The letter states: “We urge you to take this opportunity to turn the tide.
“The alternative is to leave Labour permanently damaged as an institutionally racist party.
“Our community and our country will not forgive any further failure.”