Without its natural predators present, the invasive carp can eat its way through an ecosystem, damaging native species and tourism based on fishing.
Officials are creating a barrier in Illinois to block the carp from Lake Michigan.
But now the U.S. Army is transferring management of the project to its Detroit district.
The governors of Illinois and Michigan lobbied President Trump to provide the federal funding for the project.
But in a social media post, an Army official says Michigan has been a good partner, while calling Illinois unreliable and claiming the state is delinquent on its share of payments.
Illinois Governor JB Pritzker is a harsh critic of Trump.