Genome-scale metabolic model (GEM) reconstruction aims to build organism-specific metabolic networks that accurately and coherently reflect microbial metabolic capabilities, yet constructing accurate and biologically coherent GEMs remains challenging due to the large combinatorial space of possible reactions and the indirect relationship between genomic evidence and metabolic phenotypes. Here, we propose a genome-conditioned, agent-based framework for accurate and biologically plausible GEM reconstruction. Instead of treating reconstruction as a static annotation-to-reaction mapping process or a medium-specific gap-filling problem, our framework represents both genomes and GEMs in a unified AI embedding space and formulates reconstruction as an iterative decision-making task. Given a draft metabolic network, the agent reasons over the current GEM state, genome-derived evidence, network-level metabolic context, and phenotype-derived constraints to propose targeted reaction additions and removals. Each modification is verified by flux balance analysis (FBA), enabling the system to form a closed loop between neural decision-making and symbolic biochemical validation. By incorporating both growth and no-growth phenotypes, the framework improves not only the ability to recover missing metabolic functions but also the capacity to avoid over-permissive networks that incorrectly predict growth under unsupported conditions. This design allows GEM reconstruction to move beyond isolated reaction completion toward global improvement of model accuracy, phenotype consistency, and structural plausibility. Experiments on microbial GEM reconstruction and substrate utilization prediction show that our method improves overall reconstruction accuracy and produces more coherent organism-specific metabolic models across diverse environmental conditions. More broadly, this work suggests a route from symbolic biological intelligence to artificial general intelligence (AGI), where AI agents can represent, test, and autonomously refine mechanistic models of living systems, demonstrating a step toward extending AI from the digital world to the living world.