The development and identification of best methods in fetal brain MRI analysis is crucial as we expect an outburst of studies on groupwise and longitudinal analysis of early brain development in the upcoming years. To address this critical need, in this paper, we have developed a mathematical framework for the construction of an unbiased deformable spatiotemporal atlas of the fetal brain MRI and compared it to alternative configurations in terms of similarity metrics and deformation models. Our contributions are twofold: first we suggest a novel approach to fetal brain spatiotemporal atlas construction that shows high capability in capturing anatomic variation between subjects; and second, within our atlas construction framework we evaluate and compare a set of plausible configurations for inter-subject fetal brain MRI registration and identify the most accurate approach that can potentially lead to most accurate results in population atlas construction, atlas-based segmentation, and group analysis. Our evaluation results indicate that symmetric diffeomorphic deformable registration with cross correlation similarity metric outperforms other configurations in this application and results in sharp unbiased atlases that can be used in fetal brain MRI analysis.