A Russian woman accused of trying to set up back-channel relationships with Republican politicians through the National Rifle Association was arrested and charged with not registering as a foreign agent in Washington, the Justice Department said Monday.

Maria Butina, a 29-year-old woman who has lived in Washington as a student at American University and was known as an enthusiastic gun-rights advocate, was arrested on Sunday and made a court appearance on Monday, prosecutors said. She was ordered held without bail pending...