He proposed the second of the two motions, which says Ms Berger is "continiously criticising our leader when she should be working towards a general election".
In July 2017, he wrote on Facebook Ms Berger should be "exposed for the disruptive Zionist she is".
Labour Deputy Leader Tom Watson has condemned those pushing the confidence motions against Ms Berger, saying they "bring disgrace to the party that I love".
He told the Commons: "As we unify and commit to support this bill, let us not forget our honourable colleagues on both sides of the House, the subject of death threats, the subject of racist abuse, the subject of misogynistic abuse, the subject of bullying and antisemitism.
"Let me say to the honourable colleagues facing that abuse, and in particular my friend and comrade the member for Liverpool Wavertree, that she has our solidarity, our support, as she battles the bullying and hatred from members of her own local party."
Meanwhile, John McDonnell reacted to the motions by demanding Ms Berger reject rumours she was considering leaving Labour.
The shadow chancellor said they were to do with recent media reports that Ms Berger was poised to quit the party and form a break-away party.
He told BBC Radio Four's Today programme: "It's not a deselection... It's an expression of views. If people are doing that because she's stood up against antisemitism, that's completely wrong."
But he said this was not the case on this motion, "from what I've seen on social media".
He added: "Luciana has been associated in the media with a break away party... the media have asked her to deny that and she hasn’t been clear on that.
"So, my advice to Luciana is just tell people you're not leaving Labour, you're not jumping ship... on all of this is for Luciana to just put this issue to bed."
But Mr McDonnell was condemned on social media for this response.
Holocaust Educational Trust chief executive Karen Pollock called it a "disgrace" that Mr McDonnell was "demanding loyalty... rather than addressing the racism in your party".
Labour MP Chuka Umunna said: "How about demanding her CLP treats her with the respect she deserves. How about the party deals with that racism. Words fail me. Totally unacceptable."
