CHICAGO — Asian carp, the voracious, nonnative fish whose arrival near Lake Michigan is threatening to cause havoc in the Great Lakes, are now setting off strife on land as well.

In an urgent effort to close down Chicago-area passages that could allow the unwanted fish to reach Lake Michigan, the State of Michigan is suing the State of Illinois and other entities that govern the waterways here. Minnesota, Ohio and Wisconsin have filed documents in recent days supporting Michigan’s move, and Indiana says it will soon do the same.

The new rift between these Midwestern states, which would reopen a nearly century-old legal case in the United States Supreme Court over Great Lakes waters, comes at a particularly sensitive moment — just as the numerous entities with interests in the Great Lakes had united in what lakes advocates consider some of their most significant progress in decades.

In 2008, the eight states that touch the Great Lakes helped push through a federal-state compact that bars diversion of water from the lakes unless all of the states (and the Canadian provinces involved) agree. That Great Lakes Compact, which was years in the making, at last calmed fears that other water-starved regions might tap into the lakes, which make up 20 percent of the world’s freshwater.