One of the classical approaches to automated planning is the reduction to propositional satisfiability (SAT). Recently, it has been shown that incremental SAT solving can increase the capabilities of several modern encodings for SAT-based planning. In this paper, we present a further improvement to SAT-based planning by introducing a new algorithm named PASAR based on the principles of counterexample guided abstraction refinement (CEGAR). As an abstraction of the original problem, we use a simplified encoding where interference between actions is generally allowed. Abstract plans are converted into actual plans where possible or otherwise used as a counterexample to refine the abstraction. Using benchmark domains from recent International Planning Competitions, we compare our approach to different state-of-the-art planners and find that, in particular, combining PASAR with forward state-space search techniques leads to promising results.