Accurate 3D cardiovascular models are essential for patient-specific treatment planning, medical device design, and computational hemodynamics; however, current approaches face significant limitations. Image-based reconstruction methods require high-quality medical imaging data and lack parametric control for design optimization. Procedural modeling offers geometric flexibility and systematic parameter exploration but demands specialized expertise in computational geometry and cardiovascular anatomy, making it inaccessible to clinical researchers and biomedical engineers. We present an agentic-AI framework that enables domain experts to generate anatomically accurate, fully parametric 3D cardiovascular models through iterative natural language refinements, minimizing the need for programming expertise. Our workflow leverages LLM-assisted code generation to progressively refine Python scripts that generate parameterized cardiovascular geometries as hierarchical non-uniform rational B-spline (NURBS) surface representations with anatomical constraints. This representation can be tessellated into polygonal meshes with arbitrary precision, ensuring compatibility with computational cardiovascular analysis workflows. We demonstrate the framework on patient-specific aortic geometries and valve structures reconstructed from clinical imaging data. Procedural models are fit to imaging-derived surface data by iteratively refining human-readable YAML descriptor files that the LLM originally templated. We illustrate analysis-ready deployment by coupling procedurally generated models with computational solvers to simulate patient-specific hemodynamics. This approach uniquely combines pre-trained LLM-assisted template creation, mathematically continuous representations that enable both clinical assessment and simulation, and direct parametric control via structured descriptors. The framework democratizes sophisticated geometric modeling for cardiovascular research while maintaining mathematical rigor through anatomically interpretable parameterizations.