Objective This study presents a novel deep learning-based framework for precise brain MR region segmentation, aiming to identify the location and the shape details of different anatomical structures within the brain. Materials and methods The approach uses a two-stage 3D segmentation technique on a dataset of adult subjects, including cognitively normal participants and individuals with cognitive decline. Stage 1 employs a 3D U-Net to segment 13 brain regions, achieving a mean DSC of 0.904 +/- 0.060 and a mean HD95 of 1.52 +/- 1.53 mm (a mean DSC of 0.885 +/- 0.065 and a mean HD95 of 1.57 +/- 1.35 mm for smaller parts). For challenging regions like hippocampus, thalamus, cerebrospinal fluid, amygdala, basal ganglia, and corpus callosum, Stage 2 with SegResNet refines segmentation, improving mean DSC to 0.921 +/- 0.048 and HD95 to 1.17 +/- 0.69 mm. Results Statistical analysis reveals significant improvements (p-value < 0.001) for these regions, with DSC increases ranging from 1.3 to 3.2% and HD95 reductions of 0.06-0.33 mm. Comparisons with recent studies highlight the superior performance of the performed method. Discussion The inclusion of a second stage for refining the segmentation of smaller regions demonstrates substantial improvements, establishing the framework's potential for precise and reliable brain region segmentation across diverse cognitive groups.