The MRI accelerator, a combination of a 6 MV linear accelerator with a 1.5 T MRI, facilitates continuous patient anatomy updates regarding translations, rotations and deformations of targets and organs at risk. Accounting for these demands high speed, online intensity-modulated radiotherapy (IMRT) re-optimization. In this paper, a fast IMRT optimization system is described which combines a GPU-based Monte Carlo dose calculation engine for online beamlet generation and a fast inverse dose optimization algorithm. Tightly conformal IMRT plans are generated for four phantom cases and two clinical cases (cervix and kidney) in the presence of the magnetic fields of 0 and 1.5 T. We show that for the presented cases the beamlet generation and optimization routines are fast enough for online IMRT planning. Furthermore, there is no influence of the magnetic field on plan quality and complexity, and equal optimization constraints at 0 and 1.5 T lead to almost identical dose distributions.