Background and purpose: Physiological motion impacts the dose delivered to tumours and vital organs in external beam radiotherapy and particularly in particle therapy. The excellent soft-tissue demarcation of 4D magnetic resonance imaging (4D-MRI) could inform on intra-fractional motion, but long image reconstruction times hinder its use in online treatment adaptation. Here we employ techniques from high-performance computing to reduce 4D-MRI reconstruction times below two minutes to facilitate their use in MR-guided radiotherapy. Material and methods: Four patients with pancreatic adenocarcinoma were scanned with a radial stack-of-stars gradient echo sequence on a 1.5T MR-Linac. Fast parallelised open-source implementations of the extra-dimensional golden-angle radial sparse parallel algorithm were developed for central processing unit (CPU) and graphics processing unit (GPU) architectures. We assessed the impact of architecture, oversampling and respiratory binning strategy on 4D-MRI reconstruction time and compared images using the structural similarity (SSIM) index against a MATLAB reference implementation. Scaling and bottlenecks for the different architectures were studied using multi-GPU systems. Results: All reconstructed 4D-MRI were identical to the reference implementation (SSIM > 0.99). Images reconstructed with overlapping respiratory bins were sharper at the cost of longer reconstruction times. The CPU + GPU implementation was over 17 times faster than the reference implementation, reconstructing images in 60 ± 1 s and hyper-scaled using multiple GPUs. Conclusion: Respiratory-resolved 4D-MRI reconstruction times can be reduced using high-performance computing methods for online workflows in MR-guided radiotherapy with potential applications in particle therapy.