The House of Representatives voted 171-2 on Tuesday to adopt a resolution seeking a thin strip of land leading to the river.
Georgia lawmakers say a flawed 1818 survey wrongly put the border to the south of the Tennessee River. In the resolution, Georgia offers to accept the current border with the exception of a slice of land allowing for water withdrawals from the river.
Tennessee lawmakers have so far been dismissive of the request.
Georgia is locked in a long-running water dispute with neighboring Alabama and Florida. That dispute has at times threatened metro Atlanta’s water supply, forcing officials to search for new water sources.