An electronic device may operate a fingerprint reader in a stationary finger mode in which the fingerprint reader captures a fingerprint from a user's finger while the user's finger is in a stationary position and may operate the fingerprint reader in a moving finger mode in which the fingerprint reader captures a fingerprint from the user's finger while the user is swiping the finger across the fingerprint reader. The electronic device may use the moving finger mode when performing sensitive operations such as operations related to financial transactions. The electronic device may include near field communications circuitry. When activity is detected using the near field communications circuitry, the fingerprint reader may be operated in the moving finger mode. The fingerprint sensor may be activated when a proximity sensor detects the presence of a finger. Different actions may be taken by the device in response to detection of different fingerprints.