The federal lawsuit filed Wednesday in Richland, Washington, follows a similar one Tuesday by two California counties.
Under new rules unveiled this week, Citizenship and Immigration Services will consider whether applicants have received public assistance among other factors such as education to determine whether to grant legal status.
The attorneys general argue the expansion will cause "irreparable harm" and deter noncitizens from seeking "essential" public assistance.
The lawsuit names the U.S. Department of Homeland Security. A spokesman didn't return a message Wednesday.
The states involved are: Colorado, Delaware, Illinois, Maryland, Massachusetts, Michigan, Minnesota, Nevada, New Jersey, New Mexico, Rhode Island, Virginia and Washington.
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