In a statement later on Tuesday, Benson's press secretary said she intends to appeal the judge's decision.
"Also, supporting the plaintiffs' position is that the directive does not merely provide guidance to local election officials on existing state law, as it appears to be partially inconsistent with state law", Murray wrote in the court filing on Tuesday.
Murray said the Michigan Secretary of State has failed to put her directive through the Administrative Procedures Act in order for it to be enforced as a rule.
In her memo, Benson has argued that "the presence of firearms at the polling place, clerk's office(s), or absent voter counting board may cause disruption, fear, or intimidation for voters, election workers, and others present".
Michigan gun advocates sued the Secretary of State to overturn her directive to ban open carry of firearms at the polls on 3 November.