SANTA FE, N.M.—New Mexico’s Democratic attorney general charged Republican Secretary of State Dianna Duran with embezzlement, fraud, money laundering and campaign finance violations, further widening a rift between the two over enforcement of the state’s laws governing campaigns.

Attorney General Hector Balderas’ office filed the 64-count complaint late Friday in state district court in Santa Fe. Mr. Balderas didn’t make a statement or hold a news conference to announce the complaint against Ms. Duran, one of the highest-ranking...