In real-world scenarios, social networks play a vital role in daily communication and serve as powerful channels for rapid information dissemination. However, this high degree of connectivity also facilitates the spread of rumors, underscoring the urgent need for effective rumor control mechanisms. Most existing approaches fail to adequately account for two critical aspects of real-world rumor propagation: first, that rumors typically unfold over multiple rounds, and second, that users vary in priority within practical social contexts. To address this gap, we propose a new problem formulation termed Online Adaptive Rumor Blocking with Pertinence Set (OARBP), and introduce a corresponding solution framework–the Multi-round Hybrid Greedy Framework (MHGF). This method employs an adaptive and intelligent strategy to combat multi-round rumor propagation through three core stages: a local phase, a global phase, and a realization phase. The primary objective is to select a set of truth-seed nodes that disseminate truthful information, thereby maximizing the spread of truth while ensuring sufficient coverage within high-priority user groups. Experimental evaluations conducted on eight real-world social network datasets demonstrate the efficiency and effectiveness of the proposed framework. The results indicate that our approach not only facilitates rapid truth propagation but also successfully achieves targeted protection of key users, outperforming several existing methods.