We introduce a Recursive INsertion-based Encoder (RINE), a novel approach for semantic parsing in task-oriented dialog. Our model consists of an encoder network that incrementally builds the semantic parse tree by predicting the non-terminal label and its positions in the linearized tree. At the generation time, the model constructs the semantic parse tree by recursively inserting the predicted non-terminal labels at the predicted positions until termination. RINE achieves state-of-the-art exact match accuracy on low- and high-resource versions of the conversational semantic parsing benchmark TOP, outperforming strong sequence-to-sequence models and transition-based parsers. We also show that our model design is applicable to nested named entity recognition task, where it performs on par with state-of-the-art approach designed for that task. Finally, we demonstrate that our approach is 2-3.5 times faster than the sequence-to-sequence model at inference time.