Summary: Nonmonotonic reasoning has been explored as a form of abductive reasoning where default assumptions are treated as abductive hypotheses. While the semantics and proof theories under this approach have been studied extensively, the question of how disjunctive programs may be used to reason abductively has rarely been investigated. At the center of the question is how to embed disjunctive reasoning into that of negation-as-failure. A more concrete question is about whether the elegant abductive proof procedure by Eshghi and Kowalski can be extended to answer queries for disjunctive programs, and if yes, what is the semantics that such an extended procedure computes. In this paper we answer these questions by formulating a semantics, the regular extension semantics, for disjunctive programs, and by presenting a sound and complete extension of the Eshghi-Kowalski procedure, called disjunctive EK procedure, for query answering with respect to ground disjunctive programs under this semantics.