Artificial intelligence is reshaping scientific discovery, yet its use in materials research remains limited by fragmented computational ecosystems, reproducibility challenges, and dependence on commercial large language models (LLMs). Here we introduce AGAPI (AtomGPT.org API), an open-access agentic AI platform that integrates more than eight open-source LLMs with over twenty materials-science API endpoints, unifying databases, simulation tools, and machine-learning models through a common orchestration framework. AGAPI employs an Agent-Planner-Executor-Summarizer architecture that autonomously constructs and executes multi-step workflows spanning materials data retrieval, graph neural network property prediction, machine-learning force-field optimization, tight-binding calculations, diffraction analysis, and inverse design. We demonstrate AGAPI through end-to-end workflows, including heterostructure construction, powder X-ray diffraction analysis, and semiconductor defect engineering requiring up to ten sequential operations. In addition, we evaluate AGAPI using 30+ example prompts as test cases and compare agentic predictions with and without tool access against experimental data. With more than 1,000 active users, AGAPI provides a scalable and transparent foundation for reproducible, AI-accelerated materials discovery. AGAPI-Agents codebase is available at https://github.com/atomgptlab/agapi.