We introduce an automated parameterized verification method for fault-tolerant distributed algorithms (FTDA). FTDAs are parameterized by both the number of processes and the assumed maximum number of Byzantine faulty processes. At the center of our technique is a parametric interval abstraction (PIA) where the interval boundaries are arithmetic expressions over parameters. Using PIA for both data abstraction and a new form of counter abstraction, we reduce the parameterized problem to finite-state model checking. We demonstrate the practical feasibility of our method by verifying several variants of the well-known distributed algorithm by Srikanth and Toueg. Our semi-decision procedures are complemented and motivated by an undecidability proof for FTDA verification which holds even in the absence of interprocess communication. To the best of our knowledge, this is the first paper to achieve parameterized automated verification of Byzantine FTDA.