We propose a new method for PET/MR respiratory motion compensation, which is based on a 3D-2D registration of strongly undersampled MR data and a) runs in parallel with the PET acquisition, b) can be interlaced with clinical MR sequences, and c) requires less than one minute of the total MR acquisition time per bed position. In our simulation study, we applied a 3D encoded radial stack-of-stars sampling scheme with 160 radial spokes per slice and an acquisition time of 38 s. Gated 4D MR images were reconstructed using a 4D iterative reconstruction algorithm. Based on these images, motion vector fields were estimated using our newly-developed 3D-2D registration framework. A 4D PET volume of a patient with eight hot lesions in the lungs and upper abdomen was simulated and MoCo 4D PET images were reconstructed based on the motion vector fields derived from MR. For evaluation, average SUVmean values of the artificial lesions were determined for a 3D, a gated 4D, a MoCo 4D and a reference (with ten-fold measurement time) gated 4D reconstruction. Compared to the reference, 3D reconstructions yielded an underestimation of SUVmean values due to motion blurring. In contrast, gated 4D reconstructions showed the highest variation of SUVmean due to low statistics. MoCo 4D reconstructions were only slightly affected by these two sources of uncertainty resulting in a significant visual and quantitative improvement in terms of SUVmean values. Whereas temporal resolution was comparable to the gated 4D images, signal-to-noise ratio and contrast-to-noise ratio were close to the 3D reconstructions.