A progressive group called on Republican National Committee leader Pat Rogers to step down on Friday after emails showed him telling New Mexico Gov. Susana Martinez’s staff that meeting with a group of American Indians “dishonored” Gen. George Armstrong Custer, the 19th century commander who killed scores of American Indians.

“The state is going to hell,” Rogers, who is a member of the GOP executive committee and is currently in Tampa for the RNC convention, wrote in a June 8 email released by Progress Now New Mexico. Former Republican gubernatorial candidate Col. Allen Weh “would not have dishonored Col Custer in this manner,” he wrote....