Plaintiffs in a lawsuit against a Kentucky county clerk who refuses to issue marriage licenses to same-sex couples filed a motion Monday evening arguing that she is once again violating a federal court’s orders and asking a judge to enforce them.

Rowan County Clerk Kim Davis, who objects to same-sex marriage on religious grounds, spent five days in jail earlier this month for repeatedly defying U.S. District Judge David Bunning’s order to issue licenses to all qualified couples, gay or straight. The judge then secured a commitment...