Mr Uddin, who is a vice-chair of the school’s Labour Society, and a Labour Party member, encouraged Samiha Begum to leave the contest to be general secretary of the LSE union.
In a message Mr Uddin sent to Ms Begum, seen by the JC, he wrote that fellow candidate Harry Maxwell, who is endorsed by LSE’s Jewish and Israel societies, was “running a very slick campaign”.
Mr Uddin wrote: “We discussed the other day how he is backed by Jay Stoll [a former Jewish LSE SU general secretary] and other leading Zionists around the country because they want to win back LSE and make it right wing and Zio again.
“The Zionists at LSE have two priorities this year; getting last year’s LSE Israel society president Josh Seitler to become the new UJS President, and the second is for Harry Maxwell to become Gen Sec.
“The first has already happened. If the second happens too, not only will it be awful for Muslims and pro-Palestine activists at LSE, but for Muslims and pro-Palestine activists across the whole country.
“A combination of Josh and Harry will be really damaging to all the work NUS and others are doing with BDS, Prevent and other things.”
Mr Uddin goes on to call on Ms Begum to leave the contest and avoid splitting the vote.
The complaint about the correspondence was made to Baroness Royall and Labour general secretary Iain McNicol on Wednesday morning.
It alleges that Mr Uddin’s comments amount to “antisemitic conspiracy theories by a senior member of the Labour club”.
In a lengthy explanation on his Facebook page, Mr Uddin apologised for using the word "Zio".
He wrote: "I would like to take this opportunity to apologise unreservedly to the Jewish community.
"As somebody who stands in a proud tradition of anti-racism it is utterly repugnant to me to think that I may have unwittingly appeared to endorse in any way the foul ideology of antisemitism, I am deeply sorry to all those who I have angered or offended, and I hope to have the opportunity to win back your trust in the future."
Mr Uddin wrote that it was "wrong" for him to have suggested that if Mr Maxwell won the contest it would be bad for Muslims and pro-Palestinian students.
"What I cannot accept, however, is the innuendo that my simply stating that Zionists and anti-Zionists alike will be taking an interest in the campaign is tantamount to alleging a ‘Zionist conspiracy’," he continued.
"Moreover, I am disappointed in myself that this this controversy overshadows my broader efforts to tackle antisemitism on campus."
Mr Uddin said he would be continuing his campaign to be the next general secretary.
The JC understands that LSE SU is investigating complaints about his remarks.
LSE Jewish Society said it found Mr Uddin’s reported remarks “alarming”. Members had seen comments on Facebook on Tuesday, the group said.
The claims of a Zionist conspiracy were “reminiscent of some of the most dangerous, ugly, yet unfortunately, frequently repeated antisemitic tropes of the past 100 years. It has no place on our campus”.
LSE Student Union confirmed it had not received an official complaint about the issue, but the election returning officer is understood to have received a complaint and is investigating.
