The 26-year-old made headlines last week with a maiden speech in the House of Commons in which she thanked “Jewish comrades” before decrying what she called “40 years of Thatcherism”.
She became an MP at last month’s General Election, although her seat's Labour majority fell from 8,000 to just 405 votes.
Ms Sultana studied at Birmingham University but has deleted social media posts from her time as an outspoken pro-Palestine campaigner – including comments the JC previously revealed in which she said she would “celebrate” the deaths of Tony Blair and Benjamin Netanyahu.
But in a series of further posts, Ms Sultana responded to a Union of Jewish Students member who had argued for the possibility of a peaceful resolution in the Middle East, writing: “It is your privilege that lets you sit on the fence about what’s happening.
“It is your privilege that lets you speak on stage and call for peace.”
Ms Sultana has previously been revealed to have written in support of “violent resistance” by Palestinians.
Her posts, which were written in 2015, say: "Those within the student movement who go to Zionist conferences and trips should be ashamed of themselves.
“You’re advocating a racist ideology. It’s not progressive to champion a state created through ethnic cleansing, sustained occupation, Apartheid and war crimes.
“There will come a time in the near future where those who lobby for Israel feel the same shame and regret as South African Apartheid supporters.”
In another post, Ms Sultana claimed Jewish students at Birmingham University had served in the IDF "on a gap year sort of initiative".
Some year-long courses offered to UK students by Israeli tour groups do include collaboration with the IDF – but not in the form of active service with the Israeli military.
But Ms Sultana discussed who is able to serve with the IDF in another post, writing that “you don’t even need Israeli citizenship to serve, you just need to prove you are Jewish.
“So a lot of students from my university serve because they want to – not because they have to. On a ‘gap year’ sort of initiative.”
One Jewish student who attended Birmingham University at the same time as Ms Sultana said: “Her whole raison d’etre was that Jewish students were basically privileged white people who had no right to speak out on racism or injustices around Israel/Palestine.
“Ms Sultana and her followers completely over-stepped the mark with their Palestinian activism. They routinely targeted Jewish students who objected to their way of thinking.”
The JC has approached Ms Sultana for comment.
LFI Director Jennifer Gerber said: "Labelling the Jewish people's right to self-determination as a racist ideology, and making totally false comparisons between Israel and apartheid-era South Africa, is utterly despicable and offensive.
"The whip should be withdrawn immediately while this and a series of other allegations which arose during the general election campaign are thoroughly and independently investigated."
During her time at university, Ms Sultana actively campaigned in support of the BDS movement and was involved in the University of Birmingham Students For Justice In Palestine group.
The pro-Jeremy Corbyn MP also regularly called for anti-terror laws in the UK to be scrapped and also once wrote that British police would "detain and question 'suspicious looking' people at airports either because their name has 'Muhammad' in it, they have a beard or because they are wearing a turban.”
