Open environment oriented open set model attribution of deepfake audio is an emerging research topic, aiming to identify the generation models of deepfake audio. Most previous work requires manually setting a rejection threshold for unknown classes to compare with predicted probabilities. However, models often overfit training instances and generate overly confident predictions. Moreover, thresholds that effectively distinguish unknown categories in the current dataset may not be suitable for identifying known and unknown categories in another data distribution. To address the issues, we propose a novel framework for open set model attribution of deepfake audio with rejection threshold adaptation (ReTA). Specifically, the reconstruction error learning module trains by combining the representation of system fingerprints with labels corresponding to either the target class or a randomly chosen other class label. This process generates matching and non-matching reconstructed samples, establishing the reconstruction error distributions for each class and laying the foundation for the reject threshold calculation module. The reject threshold calculation module utilizes gaussian probability estimation to fit the distributions of matching and non-matching reconstruction errors. It then computes adaptive reject thresholds for all classes through probability minimization criteria. The experimental results demonstrate the effectiveness of ReTA in improving the open set model attributes of deepfake audio.