Fault localization aims to automatically identify the cause of an error in a program by localizing the error to a relatively small part of the program. In this paper, we present a novel technique for automated fault localization via error invariants inferred by abstract interpretation. An error invariant for a location in an error program over-approximates the reachable states at the given location that may produce the error, if the execution of the program is continued from that location. Error invariants can be used for statement-wise semantic slicing of error programs and for obtaining concise error explanations. We use an iterative refinement sequence of backward-forward static analyses by abstract interpretation to compute error invariants, which are designed to explain why an error program violates a particular assertion. We demonstrate the effectiveness of our approach to localize errors in realistic C programs.