A surgeon's physiological hand tremor can significantly impact the outcome of delicate and precise retinal surgery, such as retinal vein cannulation (RVC) and epiretinal membrane peeling. Robot-assisted eye surgery technology provides ophthalmologists with advanced capabilities such as hand tremor cancellation, hand motion scaling, and safety constraints that enable them to perform these otherwise challenging and high-risk surgeries with high precision and safety. Steady-Hand Eye Robot (SHER) with cooperative control mode can filter out surgeon's hand tremor, yet another important safety feature, that is, minimizing the contact force between the surgical instrument and sclera surface for avoiding tissue damage cannot be met in this control mode. Also, other capabilities, such as hand motion scaling and haptic feedback, require a teleoperation control framework. In this work, for the first time, we implemented a teleoperation control mode incorporated with an adaptive sclera force control algorithm using a PHANTOM Omni haptic device and a force-sensing surgical instrument equipped with Fiber Bragg Grating (FBG) sensors attached to the SHER 2.1 end-effector. This adaptive sclera force control algorithm allows the robot to dynamically minimize the tool-sclera contact force. Moreover, for the first time, we compared the performance of the proposed adaptive teleoperation mode with the cooperative mode by conducting a vessel-following experiment inside an eye phantom under a microscope.