Abstract: An extended Newtonian gravitation (ENG) model was developed to explain the rotation curves in galaxies and galaxy clusters. ENG requires the knowledge of a parameter that is a function of the mass of the gravitational source. An approximate eq. for that parameter was obtained (for disk galaxies) that yields asymptotic speeds close to binned measured data. ENG yielded larger circular speeds for galaxy clusters when compared with the MOND results. A classical gravito-electromagnetic model (which neither is based on Einstein GR, nor on gravito-magnetism only) was developed which yielded asymptotic circular speeds very small compared to experimental results. However when ENG was used to develop an extended gravito-electromagnetic model, it yielded results compatible with MOND results for simulated galaxies and larger than MOND results for a simulated galaxy cluster. This model showed measurable increase in the circular speed when compared to ENG alone in the galaxy cluster. The need for modifying the Einstein field equation to address the dark matter problem in the framework of the ENG model was illustrated.