Automatic speech recognition (ASR) systems often rely on autoregressive (AR) Transformer decoder architectures, which limit efficient inference parallelization due to their sequential nature. To this end, non-autoregressive (NAR) approaches aim primarily to achieve significant decoding speedup while the maintaining recognition accuracy that is comparable to AR baselines. This paper proposes a novel NAR block-based attention mask decoder (AMD) that effectively improves decoding efficiency while maintaining ASR accuracy, and also offering flexibility in balancing the performance-efficiency trade-off on both Conformer and large language model (LLM)-based ASR systems. The proposed AMD performs parallel inference within contiguous blocks of output labels while maintaining monotonic left-to-right prediction between blocks. A one-pass beam search algorithm is designed to dynamically fuse Connectionist Temporal Classification (CTC), AR decoder, and AMD probabilities. Experiments are conducted on normal speech LS960 and DBank elderly speech across: a) The Conformer encoder-decoder ASR system with filterbank input features; b) its integration with WavLM features; and c) further advancement by integrating an LLM-based decoder. On the LS960 task, the proposed AMD empowered tripartite decoder achieves decoding speedup ratios of up to 1.44x, 1.55x, and 2.31x under the three model configurations over the CTC + AR baselines, without statistically significant WER increases. When operating with real-time factors (RTFs) comparable to the baselines, the tripartite decoder produces statistically significant WER reductions of 0.19%, 0.62% and 0.13% absolute (4.3%, 16.3%, and 3.8% relative). Similar improvements are also obtained on the DBank task.