Trustworthiness and transparency are essential for the clinical adoption of artificial intelligence (AI) in healthcare and biomedical research. Recent deep research systems aim to accelerate evidence-grounded scientific discovery by integrating AI agents with multi-hop information retrieval, reasoning, and synthesis. However, most existing systems lack explicit and inspectable criteria for evidence appraisal, creating a risk of compounding errors and making it difficult for researchers and clinicians to assess the reliability of their outputs. In parallel, current benchmarking approaches rarely evaluate performance on complex, real-world medical questions. Here, we introduce DeepER-Med, a Deep Evidence-based Research framework for Medicine with an agentic AI system. DeepER-Med frames deep medical research as an explicit and inspectable workflow of evidence-based generation, consisting of three modules: research planning, agentic collaboration, and evidence synthesis. To support realistic evaluation, we also present DeepER-MedQA, an evidence-grounded dataset comprising 100 expert-level research questions derived from authentic medical research scenarios and curated by a multidisciplinary panel of 11 biomedical experts. Expert manual evaluation demonstrates that DeepER-Med consistently outperforms widely used production-grade platforms across multiple criteria, including the generation of novel scientific insights. We further demonstrate the practical utility of DeepER-Med through eight real-world clinical cases. Human clinician assessment indicates that DeepER-Med's conclusions align with clinical recommendations in seven cases, highlighting its potential for medical research and decision support.