This paper presents a novel fingertip system with a two-layer structure for robotic hands. The outer part of the structure consists of a rubber bag filled with fluid, called the “fluid fingertip,” while the inner part consists of a rigid link mechanism called a “microgripper.” The fingertip thus is a rigid/fluid hybrid system. The fluid fingertip is effective for grasping delicate objects, that is, it can decrease the impulsive force upon contact, and absorb uncertainties in object shapes and contact force. However, it can only apply a small grasping force such that holding a heavy object with a robotic hand with fluid fingertips is difficult. Additionally, contact uncertainties including inaccuracies in the contact position control cannot be avoided. In contrast, rigid fingertips can apply considerable grasping forces and thus grasp heavy objects effectively, although this makes delicate grasping difficult. To maintain the benefits of the fluid fingertip while overcoming its disadvantages, the present study examines passively operable microgripper-embedded fluid fingertips. Our goal is to use the gripper to enhance the positioning accuracy and increase the grasping force by adding geometrical constraints to the existing mechanical constraints. Grasping tests showed that the gripper with the developed fingertips can grasp a wide variety of objects, both fragile and heavy.