Medical evidence synthesis increasingly requires published studies, real-world clinical data and structured biomedical knowledge, yet most automated systems remain centered on literature retrieval and summarization. Here we present MES, a multi-agent framework for source-grounded medical evidence synthesis. MES coordinates six specialized agents to decompose clinical questions, retrieve literature and trial evidence, generate question-specific RWE by constructing and analyzing real-world cohorts, query biomedical knowledge graphs, integrate quantitative findings and screen generated claims against their cited evidence. The framework uses evidence-based medicine taxonomies to clarify underspecified questions, adapts evidence use when sources are absent or discordant and reports unresolved gaps rather than forcing consensus. MES also provides claim-level provenance tracking and cross-agent consistency checking, allowing final reports to distinguish trial evidence, real-world associations and knowledge-graph support. We evaluated MES in two clinical use cases and across 144 clinical queries spanning six evidence-based medicine categories. MES generated structured reports that preserved source traceability, identified cross-source disagreement and communicated uncertainty across diverse clinical question types. MES provides an auditable framework for organizing, testing and contextualizing heterogeneous clinical evidence while keeping the evidentiary basis of each conclusion explicit.