Generative artificial intelligence (GAI) is increasingly used in higher education for explanation, content generation, feedback, and personalized learning. However, conventional prompt-response chatbots may provide insufficient support for complex academic tasks requiring planning, evidence organization, comparison, justification, verification, and reflection. This study proposes the Agentic GAI-Supported Learning Framework for Higher Education (AGAI-HE), which positions GAI agents as bounded, human-supervised learning partners rather than substitutes for students or instructors. The framework compares traditional e-learning, GAI-chatbot-supported learning, and GAI-agent-supported learning. Agentic support covers task contracting and interpretation, decomposition and planning, evidence organization, alternative generation, comparison and decision, feedback and refinement, and learner verification and reflection. It also incorporates human supervision, academic integrity, privacy safeguards, and instructor validation. An exploratory perception-based validation involving 130 students in an e-commerce learning context found that both AI-supported conditions were rated more positively than traditional e-learning for learning enhancement, personalization, decision-making support, and workflow organization. However, the difference between GAI agents and GAI chatbots was not statistically significant for the matched composites. The findings provide initial perception-based support for agentic GAI but do not demonstrate superior learning outcomes. Its educational value depends on making multi-step reasoning more structured, visible, verifiable, and accountable.