The use of iterative pose refinement is a critical processing step for 6D object pose estimation, and its performance depends greatly on one's choice of image representation. Image representations learned via deep convolutional neural networks (CNN) are currently the method of choice as they are able to robustly encode object keypoint locations. However, CNN-based image representations are computational expensive to use for iterative pose refinement, as they require that image features are extracted using a deep network, once for the input image and multiple times for rendered images during the refinement process. Instead of using a CNN to extract image features from a rendered RGB image, we propose to directly render a deep feature image. We call this deep texture rendering, where a shallow multi-layer perceptron is used to directly regress a view invariant image representation of an object. Using an estimate of the pose and deep texture rendering, our system can render an image representation in under 1ms. This image representation is optimized such that it makes it easier to perform nonlinear 6D pose estimation by adding a differentiable Levenberg-Marquardt optimization network and back-propagating the 6D pose alignment error. We call our method, RePOSE, a Real-time Iterative Rendering and Refinement algorithm for 6D POSE estimation. RePOSE runs at 71 FPS and achieves state-of-the-art accuracy of 51.6% on the Occlusion LineMOD dataset - a 4.1% absolute improvement over the prior art, and comparable performance on the YCB-Video dataset with a much faster runtime than the other pose refinement methods.