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Motion correction is an essential preprocessing step in functional Magnetic Resonance Imaging (fMRI) of the fetal brain with the aim to remove artifacts caused by fetal movement and maternal breathing and consequently to suppress erroneous signal correlations. Current motion correction approaches for fetal fMRI choose a single 3D volume from a specific acquisition timepoint with least motion artefacts as reference volume, and perform interpolation for the reconstruction of the motion corrected time series. The results can suffer, if no low-motion frame is available, and if reconstruction does not exploit any assumptions about the continuity of the fMRI signal. Here, we propose a novel framework, which estimates a high-resolution reference volume by using outlier-robust motion correction, and by utilizing Huber L2 regularization for intra-stack volumetric reconstruction of the motion-corrected fetal brain fMRI. We performed an extensive parameter study to investigate the effectiveness of motion estimation and present in this work benchmark metrics to quantify the effect of motion correction and regularised volumetric reconstruction approaches on functional connectivity computations. We demonstrate the proposed framework's ability to improve functional connectivity estimates, reproducibility and signal interpretability, which is clinically highly desirable for the establishment of prognostic noninvasive imaging biomarkers. The motion correction and volumetric reconstruction framework is made available as an open-source package of NiftyMIC.