The iterative and incremental nature of software development using models typically makes a model of a system incomplete (i.e., partial) until a more advanced and complete stage of development is reached. Existing model execution approaches (interpretation of models or code generation) do not support the execution of partial models. Supporting the execution of partial models at the early stages of software development allows early detection of defects, which can be fixed more easily and at a lower cost. This paper proposes a conceptual framework for the execution of partial models, which consists of three steps: static analysis, automatic refinement, and input-driven execution. First, a static analysis that respects the execution semantics of models is applied to detect problematic elements of models that cause problems for the execution. Second, using model transformation techniques, the models are refined automatically, mainly by adding decision points where missing information can be supplied. Third, refined models are executed, and when the execution reaches the decision points, it uses inputs obtained either interactively or by a script that captures how to deal with partial elements. We created an execution engine called PMExec for the execution of partial models of UML-RT (i.e., a modeling language for the development of soft real-time systems) that embodies our proposed framework. We evaluated PMExec based on several use-cases that show that the static analysis, refinement, and application of user input can be carried out with reasonable performance and that the overhead of approach, which is mostly due to the refinement and the increase in model complexity it causes, is manageable. We also discuss the properties of the refinement formally and show how the refinement preserves the original behaviors of the model.