Accurate segmentation of organs and lesions remains a core challenge in medical imaging due to structural heterogeneity and limited annotated data. Traditional CNN-based architectures like U-Net struggle with limited receptive fields, while Transformer-based models, though effective in modeling long-range dependencies, require extensive data and training. To address these limitations, we propose Conv-TABMamba, a hybrid architecture that integrates convolutional layers with a novel sequence modeling module, Tri-Axis Bidirectional Mamba (TABMamba). The early encoder stages use standard 3 × 3 × 3 convolutions to exploit inductive biases and spatial invariance, while the later stages adopt TABMamba to efficiently model global dependencies across three spatial axes. This design achieves a balance between local detail preservation and global context modeling. Conv-TABMamba is validated on six diverse 3D medical imaging datasets, including CT and MRI scans from LiTS, ATLAS, three public benchmarks, and one private dataset. Experimental results demonstrate that Conv-TABMamba achieves state-of-the-art or superior performance compared to recent advanced models in segmentation accuracy.