For implementing correct systems, handling and recovering from exceptional situations is important but challenging for ensuring correct interactions among distributed objects which are processing concurrently. To focus on exploring novel handling constructs for actor-based programming languages, we study ABS, an actor-based concurrent modeling language with an underlying executable formal semantics. This paper introduces multi-party session blocks with recovery handlers for exceptions into ABS. With this novel construct, we verify the correctness of interactions among objects within a session block. Program correctness is ensured by specifying invariants as pre- and post-conditions, called session contracts, for such a block, which is more expressive than the existing class invariant proof system for ABS. We present the extension of ABS with a try-catch-finally construct and class session recovery blocks that handle uncaught exceptions.