This paper extends the result of Caminada and Schulz [6, 7] by showing that assumption-based argumentation can represent not only normal logic programs, but also disjunctive logic programs. For this, we incorporate a previous work of ours (see [19, 20]), in which reasoning with assumption-based argumentation frameworks is based on certain core logics and the strict/defeasible assumptions may be arbitrary formulas in those logics. In our case, the core logic respects some inference rules for disjunction, which allows disjunctions in the heads of the programs’ rules to be handled properly.