The annotation of patient organs is a crucial part of various diagnostic and treatment procedures, such as radiotherapy planning. Manual annotation is extremely time-consuming, while its automation using modern image analysis techniques has not yet reached levels sufficient for clinical adoption. This paper investigates the idea of semi-supervised medical image segmentation using human gaze as interactive input for segmentation correction. In particular, we fine-tuned the Segment Anything Model in Medical Images (MedSAM), a public solution that uses various prompt types as additional input for semi-automated segmentation correction. We used human gaze data from reading abdominal images as a prompt for fine-tuning MedSAM. The model was validated on a public WORD database, which consists of 120 CT scans of 16 abdominal organs. The results of the gaze-assisted MedSAM were shown to be superior to the results of the state-of-the-art segmentation models. In particular, the average Dice coefficient for 16 abdominal organs was 85.8\%, 86.7\%, 81.7\%, and 90.5\% for nnUNetV2, ResUNet, original MedSAM, and our gaze-assisted MedSAM model, respectively.