Establishing eye contact is the fundamental key to begin any interaction between human-human and robot-human. Two approaches are available to develop an eye contact mechanism for robot-human interaction, such as simplex and duplex. The two most critical tasks: gaze crossing and gaze awareness, are prerequisite to implementing an active eye contact mechanism in any approach. However, most past robot-human interaction studies implemented a gaze crossing function to develop eye contact in the simplex mode where a robot holds for the human to initiate the communication. However, implementing gaze crossing alone is inadequate to create an active eye contact episode; the gaze awareness function also essential to achieve. This paper aims to develop a mechanism of duplex eye contact for robot-human inter-communication satisfying both functions. This work proposes a conceptual model of a duplex eye contact mechanism considering two cases: human initiative (where the human starts communication with the robot) and robot initiative (where the robot starts the communication with the participant) to achieve a duplex eye contact mechanism. Moreover, a simple robotic system is developed consisting of four software constituents: face detection module, gaze detection and tracking module, gaze awareness module, and robot response and control module to implement the conceptual model of duplex eye contact. Several preliminary experiments are performed to extract necessary cues for designing the duplex eye contact mechanism's behavioural protocol and present their results to show the usefulness of extracted cues. Moreover, the robotic framework results in a scenario (e.g., reading the book) with the proposed duplex eye contact mechanism are presented. The results show that the proposed scheme achieved 92% and 86% accuracy for human initiative case and robot initiative case, respectively in making eye contact.