Most publicly accessible remote sensing data suffer from low resolution, limiting their practical applications. To address this, we propose a diffusion model guided by neural operators for continuous remote sensing image super-resolution (NeurOp-Diff). Neural operators are used to learn resolution representations at arbitrary scales, encoding low-resolution (LR) images into high-dimensional features, which are then used as prior conditions to guide the diffusion model for denoising. This effectively addresses the artifacts and excessive smoothing issues present in existing super-resolution (SR) methods, enabling the generation of high-quality, continuous super-resolution images. Specifically, we adjust the super-resolution scale by a scaling factor s, allowing the model to adapt to different super-resolution magnifications. Furthermore, experiments on multiple datasets demonstrate the effectiveness of NeurOp-Diff. Our code is available at https://github.com/zerono000/NeurOp-Diff.