Nowadays, e-government has emerged as a government policy to improve the quality and efficiency of public administrations. In order to improve government-citizen interactions, the government agencies are providing a wide spectrum of online services. However, a single service may not be able to serve citizens' needs, but a combination of web services can serve the purpose. It is an important task to solve the problem of finding such a combination, called Web Service Composition. Building composite web services can save significant time and cost for developing new applications and enhancing the interoperability and collaboration among administrations. This paper proposes a Framework for dynamic composition of web services using an approach based on modeling the semantic relationship between the involved web services through a directed graph. It takes into consideration functional and nonfunctional attributes to enable the computation of relevant and most suitable service compositions for some service request.