Mary Lockhart appeared to question whether Israel’s secret service Mossad was involved in a campaign to undermine Jeremy Corbyn’s leadership of the party in a social media post.
Her comments prompted an angry reaction and the initial post has now been deleted.
A Labour spokesperson 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.
“All complaints about anti-semitism are fully investigated in line with our rules and procedures and any appropriate disciplinary action is taken.”
Ms Lockhart represents Lochgelly, Cardenden and Benarty on the Fife Council.
Her initial post said: “If it is a Mossad assisted campaign to prevent the election of a Labour government pledged to recognise Palestine as a state, it is unacceptable interference in the democracy of Britain.”
But she removed the post on Monday evening while the investigation into the issue was carried out.
In a Facebook statement, she said: “Following my suspension from the Labour Party to allow consideration of whether or not one of my Facebook posts breached the Labour Party’s rules in respect of anti-semitism, I have deleted the post.
“I will not be commenting further on this (or) any other matter until a judgement has been made. I remain a supporter of the Labour Party and of its current leadership.”
Mr Corbyn has been under fire over the failure of Labour to adopt International Holocaust Remembrance Alliance’s (IHRA) definition of anti-semitism in its entirety, including working examples provided by the IHRA definition.
But three leading Jewish newspapers described the failure to embrace the IHRA definition in full as “sinister”.
Labour leader Richard Leonard has so far been silent on the issue, but Scottish MSPs Monica Lennon, Jackie Baillie, Anas Sarwar, Daniel Johnson and Colin Smyth have all expressed their support for the international definition to be adopted.
Ms Baillie, the party’s economy spokeswoman, said adopting the IHRA definition
was “the right thing to do” on social media, while health spokesman Mr Sarwar said the party “must adopt the IHRA definition of anti-semitism now”.