End-to-end speaker diarization approaches have shown exceptional performance over the traditional modular approaches. To further improve the performance of the end-to-end speaker diarization for real speech recordings, recently works have been proposed which integrate unsupervised clustering algorithms with the end-to-end neural diarization models. However, these methods have a number of drawbacks: 1) The unsupervised clustering algorithms cannot leverage the supervision from the available datasets; 2) The K-means-based unsupervised algorithms that are explored often suffer from the constraint violation problem; 3) There is unavoidable mismatch between the supervised training and the unsupervised inference. In this paper, a robust generic neural clustering approach is proposed that can be integrated with any chunk-level predictor to accomplish a fully supervised end-to-end speaker diarization model. Also, by leveraging the sequence modelling ability of a recurrent neural network, the proposed neural clustering approach can dynamically estimate the number of speakers during inference. Experimental show that when integrating an attractor-based chunk-level predictor, the proposed neural clustering approach can yield better Diarization Error Rate (DER) than the constrained K-means-based clustering approaches under the mismatched conditions.