End-to-end neural diarization (EEND) with encoder-decoder-based attractors (EDA) is a promising method to handle the whole speaker diarization problem simultaneously with a single neural network. While the EEND model can produce all frame-level speaker labels simultaneously, it disregards output label dependency. In this work, we propose a novel EEND model that introduces the label dependency between frames. The proposed method generates non-autoregressive intermediate attractors to produce speaker labels at the lower layers and conditions the subsequent layers with these labels. While the proposed model works in a non-autoregressive manner, the speaker labels are refined by referring to the whole sequence of intermediate labels. The experiments with the two-speaker CALLHOME dataset show that the intermediate labels with the proposed non-autoregressive intermediate attractors boost the diarization performance. The proposed method with the deeper network benefits more from the intermediate labels, resulting in better performance and training throughput than EEND-EDA.