The Republican Van Hollen filed the motion Monday in the 7th Circuit Court of Appeals.
U.S. District Judge Barbara Crabb struck down the state's ban on Friday, but her ruling caused confusion because she didn't specifically tell county and state officials whether they could issue marriage licenses to same-sex couples.
Clerks in Madison and Milwaukee immediately began issuing licenses.
Crabb has scheduled a Monday afternoon hearing to consider Van Hollen's request late Friday to put her decision on hold and stop clerks from issuing licenses.
He filed a similar request Monday in federal appeals court.