The generation of high-quality, animatable 3D head avatars from text has enormous potential in content creation applications such as games, movies, and embodied virtual assistants. Current text-to-3D generation methods typically combine parametric head models with 2D diffusion models using score distillation sampling to produce 3D-consistent results. However, they struggle to synthesize realistic details and suffer from misalignments between the appearance and the driving parametric model, resulting in unnatural animation results. We discovered that these limitations stem from ambiguities in the 2D diffusion predictions during 3D avatar distillation, specifically: i) the avatar's appearance and geometry is underconstrained by the text input, and ii) the semantic alignment between the predictions and the parametric head model is insufficient because the diffusion model alone cannot incorporate information from the parametric model. In this work, we propose a novel framework, AnimPortrait3D, for text-based realistic animatable 3DGS avatar generation with morphable model alignment, and introduce two key strategies to address these challenges. First, we tackle appearance and geometry ambiguities by utilizing prior information from a pretrained text-to-3D model to initialize a 3D avatar with robust appearance, geometry, and rigging relationships to the morphable model. Second, we refine the initial 3D avatar for dynamic expressions using a ControlNet that is conditioned on semantic and normal maps of the morphable model to ensure accurate alignment. As a result, our method outperforms existing approaches in terms of synthesis quality, alignment, and animation fidelity. Our experiments show that the proposed method advances the state of the art in text-based, animatable 3D head avatar generation.