Strong representations of target speakers can help extract important information about speakers and detect corresponding temporal regions in multi-speaker conversations. In this study, we propose a neural architecture that simultaneously extracts speaker representations consistent with the speaker diarization objective and detects the presence of each speaker on a frame-by-frame basis regardless of the number of speakers in a conversation. A speaker representation (called z-vector) extractor and a time-speaker contextualizer, implemented by a residual network and processing data in both temporal and speaker dimensions, are integrated into a unified framework. Tests on the CALLHOME corpus show that our model outperforms most of the methods proposed so far. Evaluations in a more challenging case with simultaneous speakers ranging from 2 to 7 show that our model achieves 6.4% to 30.9% relative diarization error rate reductions over several typical baselines.