Councillor Mohammed Pappu, who represents the Blackwall and Cubitt Town ward, shared the posts on social networking website Facebook.
One post shared by the councillor claims Israel had carried out the 9/11, London bombings and the Paris terrorist attacks.
Cllr Pappu was a member of the overview and scrutiny committee as well as vice chair of the grants scrutiny sub-committee.
He resigned from the cabinet posts yesterday.
The national party has suspended Cllr Pappu from the party pending an investigation and he is currently serving as an independent councillor.
Tower Hamlets mayor John Biggs said: “I’m very clear that these views are incompatible with being a Labour Party member.
“They fall far below the standard we would expect from a Labour member and I am pleased the national Party is taking action.
“I note that Councillor Pappu has apologised and resigned from his scrutiny roles on the council, and he will need to explain his decision to share these posts.”
A spokesman for Tower Hamlets Council added: “Any form of antisemitism, racism or bigotry is completely unacceptable.
“We will thoroughly investigate any alleged breaches of our code of conduct and the standards we expect from councillors.”
Last month Tower Hamlets Council voted to adopt the definition of antisemitism as set out by the International Holocaust Remembrance Alliance.
A Labour party spokeswoman said: “The Labour Party takes all complaints of anti-Semitism extremely seriously and we are committed to challenging and campaigning against it in all its forms.
“Mohammed Pappu has been suspended from the Party pending investigation.”