Moore was expelled as chief justice for refusing to move the monument out of the state judicial building's rotunda after a judge ruled it was an unconstitutional display.
The veterans group, based in Houston, announced its plan Thursday on the Web site of a pastor who is one of its members.
The 5,280-pound granite monument has been locked in a storage closet in the state courthouse since August, when the eight associate justices ordered it removed to comply with the federal judge's order.
The veterans group, called American Veterans Standing for God and Country (search), plans to begin the tour Monday in Tennessee and cover several states in the West, Great Plains, South and East. The goal is to drop the monument off at the U.S. Capitol, where Moore has asked Congress to display the monument prominently, said Wiley Drake, a pastor and member of the veterans group.