Cartesian control algorithms are presented for six degree of freedom (6-DOF) force-reflecting hand-controllers (FRHCs) used for simultaneous operator position/orientation (or rate) commands to a virtual reality (VR) system and virtual force/moment kinesthetic reflection to the operator. The commands and kinesthetic feedback are transferred in Cartesian space. The task force/moment (wrench) dominates while features are provided to reduce operator loading: virtual payload and FRHC gravity compensation, input channels to easily separate 6-DOF inputs with one hand, constant-force return-to-center, and FRHC damping to improve relative stability. In experimental implementation, the "VR system" was a real remotely located teleoperated robotic system with real sensed task wrenches. Experimental results show that the algorithms are effective for reduced contact wrenches and increased telepresence quality in practical tasks. The methods in this paper are suitable for kinesthetic haptic display in virtual environments.