Mr Mohammed apologised “unreservedly” for sharing the post in a tweet he sent on Wednesday.
He has written the chief whip of Lambeth, Jane Edbrooke, asking for his post to be looked into as a disciplinary matter.
“I apologise unreservedly. I completely accept that I have hurt the Jewish community through my action,” he wrote in a letter to Ms Edbrooke.
“I apologise to friends who I have offended. I apologise to constituents I have offended. And I apologise to my Labour colleagues who fight racism every day. I have let down lots of people.”
Mr Mohammed said he posted the video without recognising it contained antisemitic content.
“This was a stupid and thoughtless thing to do and I recognise that it was an antisemitic act. It was totally unacceptable and it was my mistake which I do not shy away from,” he wrote.
The councillor, who is a member of his council's Equality Impact Assessment Panel and the Faiths Together in Lambeth group, said he was committed to working with all faiths, “in particular the Jewish community to learn and to tackle antisemitism in all its forms.”
He said he would write to Synagogues in Lambeth to “personally apologise” for his post and said that we wanted to “listen and learn from them.”
Jewish people responded by thanking him for his apology, with one saying: "I applaud your courage."
