Pressure is mounting on pro-Jeremy Corbyn campaign group Momentum as the organisation's vice-chair faces fresh anti-Semitism allegations.
Transport union the TSSA has warned it will "reconsider" its support for Momentum if Jackie Walker is still in her post next Thursday (6 October).
The move could leave the left-wingers without a headquarters as the TSSA provides office space for Momentum.
"I am deeply saddened that a fellow member of our Labour and trade union family holds such anti-Semitic views," said Manuel Cortes, the general secretary of the TSSA.
"Jeremy rightly spoke yesterday of the urgent need for our party to unite so we can take on the Tories. Frankly, we can't do this when people who hold such abhorrent racist views are allowed to remain active within our Party.
"I am asking Jackie that in the interests of unity she resigns at once from our Party and also as vice-chair of Momentum.
"If she doesn't, both the Labour Party and Momentum need to act to get rid of her at once. Furthermore, TSSA will reconsider our union's support for Momentum if she is still in post by this time next week."
The row broke out after Walker apparently and wrongly claimed that Holocaust Memorial Day does not include non-Jewish genocide victims and that, proportionately speaking, Jews were not the main victim of the Nazis' reign of terror.
"In the [training] session, a number of Jewish people, including me, asked for definitions of anti-Semitism," Walker said, referring to a training session on anti-Semitism held at the Labour conference in September.
"This is a subject of much debate in the Jewish community. I support David Schneider's definition and utterly condemn anti-Semitism.
"I would never play down the significance of the Shoah. Working with many Jewish comrades, I continue to seek to bring greater awareness of other genocides, which are too often forgotten or minimised.
"If offence has been caused, it is the last thing I would want to do and I apologise."
Walker was suspended from Labour earlier this year for blaming Jews for being the "chief financiers" of the slave trade. Labour later lifted the suspension after an investigation.
A source close to Momentum told IBTimes UK the group's national executive committee will meet on Monday to discuss Walker's future.