Fetal MRI offers a broad spectrum of applications, including the investigation of fetal brain development and facilitation of early diagnosis. However, image quality is often compromised by motion artifacts arising from both maternal and fetal movement. To mitigate these artifacts, fetal MRI typically employs ultrafast acquisition sequences. This results in the acquisition of three (or more) orthogonal stacks along different spatial axes. Nonetheless, inter-slice motion can still occur. If left uncorrected, such motion can introduce artifacts in the reconstructed 3D volume. Existing motion-correction approaches often rely on a two-step iterative process involving registration followed by reconstruction. They tend to detect and remove a large number of misaligned slices, resulting in poor reconstruction quality. This paper proposes a novel reconstruction-independent method for motion correction. Our approach benefits from the intersection of orthogonal slices and estimates motion for each slice by minimizing the difference between the intensity profiles along their intersections. To address potential misalignments, we present an innovative machine learning-based classifier for identifying misaligned slices. The parameters of these slices are then corrected using a multistart optimization approach. Quantitative evaluation on simulated datasets demonstrates very low registration errors. Qualitative analysis on real data further highlights the effectiveness of our approach compared to state-of-the-art methods.