A system and a method for performing 2D on-screen user gaze estimation using an input facial image of a user captured using a camera associated to a processing device having a display. The method and system allow automated user calibration through automatic recording of calibration samples each including a calibration facial image of the user and an interaction point corresponding to a point on the display where an occurrence of a user interaction was detected when the corresponding calibration image was captured. The system and method also optimize user-specific parameters using the calibration samples by iteratively minimizing a total difference between the interaction points of a plurality of the calibration samples and corresponding 2D gaze estimation results and convert an estimated 3D gaze direction into a 2D gaze estimation result corresponding to a point on the display, by applying the users-specific parameters.