The National Union of Students (NUS) is embroiled in a fresh anti-Semitism row after three candidates holding or running for positions on its executive committee were revealed to have made offensive comments.

In online posts seen by The Independent, one current member of the union’s National Executive Council shared a video mocking Jews as having big noses and being tight with money, while another publicly suggested Jewish people are tight-fisted and said he wanted to destroy Israel.

A third, who is seeking a position on the union’s executive in elections being held this week, wrote an offensive Twitter message referring to Jews and using the phrase “Heil Hitler”.

The Independent can also reveal that, during her time as a student at the University of Birmingham, Malia Bouattia, the current NUS president, was involved in hosting a play called “Seven Jewish Children” that has been widely criticised as anti-Semitic.

Ms Bouattia, who is seeking re-election, was last year accused of “outright racism” by the House of Commons Home Affairs Select Committee over comments she made relating to Israel. She had claimed the University of Birmingham was a “Zionist outpost” and criticised “Zionist-led media outlets”.

The revelations come amid mounting concern about levels of anti-Semitism on university campuses. A survey by the NUS last month found a quarter of Jewish students in the UK live in fear of an anti-Semitic attack, while two thirds who had been the victim of crime at their place of study said they were targeted because of their faith.

The NUS annual conference, where it will elect its national officers for the coming year, begins in Brighton on Tuesday. Despite the deepening worries about anti-Semitism, a number of candidates seeking office have a history of making anti-Jewish and anti-Israeli comments.

Ali Milani, who is currently a member of the union’s National Executive and is running to be its Vice President for Union Development, was accused of “deeply anti-Semitic” remarks after tweets emerged from 2012 and 2013 in which he said Israel has “no right to exist” and is “a land built on ethnic cleansing and colonialism”.

Mr Milani, who is also president of Brunel University students’ union, also made a comment about Jews and money, tweeting: “Nah u won’t mate, it’ll cost you a pound #Jew”.

Mr Milani also appeared to defend the terrorist group Hamas firing rockets into Israel, writing: “Oh fuck off! Hamas firing into southern Israel was a retaliation!”

And he threatened violence against supporters of Israel, writing: “Just heard someone say ‘Palestine. It’s what they used to call Israel’. Is a punch in the throat justified?”

Another candidate running for a place on the NUS’ National Executive Council, Sean O’Neill, posted on Twitter in 2012 using the hashtags “heilhitler” and “fuckslutskilljews” – apparently in an attempt at humour.

Meanwhile, another current NUS officer, LGBT+ Officer Noorulann Shahid, who uses the pronouns they/them, posted a link on Twitter to a comedy video that includes a number of anti-Semitic tropes and said they had “laughed out loud” at the clip.

The video, titled “Black and Jewish”, is a parody of rapper Wiz Khalifa’s song “Black and Yellow” and makes jokes about Jews having big noses and being stingy. It features two black women dressing up in traditional Jewish attire and singing lyrics including “my ass and nose, they’re both big” and “don’t spend no money but you know I’m rich”. The tweet dates from 2012.

Mr Milani, Mr O Neill and Shahid, who are all part of a left-wing grouping that includes Ms Bouattia, have apologised for their comments.

But Josh Nagli, campaigns director at the Union of Jewish Students, said he was “appalled by these absolutely disgraceful comments, all of which are extremely offensive to Jewish students.”

“The regularity of anti-Semitic comments being made by candidates is exceptionally worrisome and shows complete disregard for the welfare of Jewish students, as well as for the anti-racist, anti-fascist values that NUS and many of these individuals claim to uphold – particularly when those comments invoke the memory of the Holocaust”, he said.

“These candidates should do the right thing now and step down from their elections.

“These comments should not be seen in isolation; they are reflective of a wider culture of wilful tolerance towards anti-Semitism from members of the far left of the student movement that has been present for a number of years.”

“A year on from her election, Jewish students are still waiting for an adequate apology from the current NUS President. From her and from others in the movement, there is complete disdain shown towards anti-Semitism, with many questioning its very existence on campus and in society, undermining Jewish students’ right to define what they deem anti-Semitic.”