High-resolution medical images can provide more detailed information for better diagnosis. Conventional medical image super-resolution relies on a single task which first performs the extraction of the features and then upscaling based on the features. The features extracted may not be complete for super-resolution. Recent multi-task learning,including reconstruction and super-resolution, is a good solution to obtain additional relevant information. The interaction between the two tasks is often insufficient, which still leads to incomplete and less relevant deep features. To address above limitations, we propose an iterative collaboration network (ICONet) to improve communications between tasks by progressively incorporating reconstruction prior to the super-resolution learning procedure in an iterative collaboration way. It consists of a reconstruction branch, a super-resolution branch, and a SR-Rec fusion module. The reconstruction branch generates the artifact-free image as prior, which is followed by a super-resolution branch for prior knowledge-guided super-resolution. Unlike the widely-used convolutional neural networks for extracting local features and Transformers with quadratic computational complexity for modeling long-range dependencies, we develop a new residual spatial-channel feature learning (RSCFL) module of two branches to efficiently establish feature relationships in spatial and channel dimensions. Moreover, the designed SR-Rec fusion module fuses the reconstruction prior and super-resolution features with each other in an adaptive manner. Our ICONet is built with multi-stage models to iteratively upscale the low-resolution images using steps of 2x and simultaneously interact between two branches in multi-stage supervisions.