The UCU has been criticised by Jewish groups after delegates at its recent congress voted to reject a working definition of anti-Semitism produced by the European Union Monitoring Centre on Racism and Xenophobia.
The UCU motion says that the working definition "confuses criticism of Israeli government policy and actions with genuine anti-Semitism" and "is being used to silence debate about Israel and Palestine on campus".
The motion, proposed by the UCU's national executive committee, says the union "will make no use of the definition (eg, in educating members or dealing with internal complaints)".
The UCU has previously attracted criticism from Jewish groups for motions proposing an academic boycott of Israel, although no such motions were raised at this year's congress.
Vivian Wineman, president of the Board of Deputies of British Jews, wrote to vice-chancellors on 1 June.
"Following these developments, and in light of UCU's history of behaviour, we now believe it to be an institutionally racist organisation," he writes.
Mr Wineman adds that since its formation in 2006, the UCU "has been obsessed with Jews and Israel".
The boycott debate "has poisoned the atmosphere inside UCU and led to many Jewish members feeling harassed for their beliefs and identities", he argues.
He adds: "If UCU refuses to address claims of institutional racism, then we would ask that you reconsider whether formal union recognition...is appropriate at all".
The UCU says it has contacted the Jewish Leadership Council to suggest a meeting but has not received a reply.
Sally Hunt, the UCU general secretary, says in a letter to the council that the motion "does not affect the union's...implacable opposition to anti-Semitism itself".