The Internet of Things (IoT) is a heterogeneous information sharing and access platform that provides services in a pervasive manner. Task and computation offloading in the IoT helps to improve the response rate and the availability of resources. Task offloading in a service-centric IoT environment mitigates the complexity in response delivery and request processing. In this paper, the state-based task offloading method (STOM) is introduced with a view to maximize the service response rate and reduce the response time of the varying request densities. The proposed method is designed using the Markov decision-making model to improve the rate of requests processed. By defining optimal states and filtering the actions based on the probability of response and request analysis, this method achieves less response time. Based on the defined states, request processing and resource allocations are performed to reduce the backlogs in handling multiple requests. The proposed method is verified for the response rate and time for the varying requests and processing servers through an experimental analysis. From the experimental analysis, the proposed method is found to improve response rate and reduce backlogs, response time, and offloading factor by 11.5%, 20.19%, 20.31%, and 8.85%, respectively.