A councillor has stood down from the authority's executive committee following claims he shared racist material on Facebook.
Wrexham Council said it was looking into claims children's services lead member Bill Baldwin shared several offensive posts in 2018.
Anti-racism group Hope Not Hate said one included a meme originally from a branch of the British National Party.
Mr Baldwin said he had stood aside voluntarily during the investigation.
Wrexham Council said it took racism seriously.
One of the posts Mr Baldwin, who represents Little Acton, allegedly shared was titled "how the British have passively succumbed to the Muslim invasion".
Hope Not Hate said the posts created "prejudice and hostility" and called for him to permanently stand down from his executive role.
A spokesman added: "It is inexcusable that a councillor responsible for children's services is abusing their public position by using social media to distribute racist material."
The posts were brought to the council's attention after being sent to the Local Democracy Reporting Service by a member of the public.
A council spokeswoman said elected members must adhere to a code of conduct and follow social media guidelines.
She said: "When instances such as these are brought to our attention, which may be in breach of these, they will be investigated and appropriate action taken."
Mr Baldwin is a member of the Wrexham Independent Group which runs the council in coalition with the Conservatives and another independent group.