Robots executing force controlled tasks require accurate perception of the applied force in order to guarantee precision. However, dynamic motions generate non-contact forces due to the inertia. These non-contact forces can be regarded as disturbances to be removed such that only the forces generated by contacts with the environment remain. This paper presents an observer based on a recurrent neural network that estimates the non-contact forces measured by a force-torque sensor attached at the end-effector of a robotic arm. The approach is proven to also work with an external load attached to the robotic arm. The recurrent neural network observer uses signals from the joint encoders of the robotic arm and a low-cost inertial measurement unit to estimate the wrenches (i.e. forces and torques) generated due to gravity, inertia, centrifugal and Coriolis forces. The accuracy of the proposed observer is experimentally evaluated by comparing the measurements of the attached force-torque sensor to the observer's non-contact forces estimation. Additionally, the pure contact force estimation is evaluated against an external force-torque sensor.