The design principle of composability among Web services is one of the most crucial reasons for the success and popularity of Web services. However, achieving error-free automatic Web service composition is still a challenge. In this paper, we propose a recursive composition based modeling and verification technique for Web service interaction. The application of recursive composition over a Web service with respect to a given set of Web services yields a recursive composition interaction graph (RCIG). In order to capture the requirement specifications of a Web service interaction scenario, we propose recursive composition specification language (RCSL) as a requirement specification language. Further, we employ the proposed RCIG as an interpretation model to interpret the semantics of a RCSL formula. Our verification technique is based on the generation and analysis of all possible interaction patterns. Performance evaluation results, provided in this paper, show that our proposition is implementable for the real world applications. The key advantages of the proposed approach are: (i) it does not require explicit system modeling as in model checking based approaches, (ii) it captures primitive characteristics of Web service interaction patterns, such as recursive composition, sequential and parallel flow, etc, and (iii) it supports automatic composition of services.