Person or identity verification has been recently gaining a lot of attention using audio-visual fusion as faces and voices share close associations with each other. Conventional approaches based on audio-visual fusion rely on score-level or early feature-level fusion techniques. Though existing approaches showed improvement over unimodal systems, the potential of audio-visual fusion for person verification is not fully exploited. In this paper, we have investigated the prospect of effectively capturing both the intra- and inter-modal relationships across audio and visual modalities, which can play a crucial role in significantly improving the fusion performance over unimodal systems. In particular, we introduce a recursive fusion of a joint cross-attentional model, where a joint audio-visual feature representation is employed in the cross-attention framework in a recursive fashion to progressively refine the feature representations that can efficiently capture the intra-and inter-modal relationships. To further enhance the audio-visual feature representations, we have also explored BLSTMs to improve the temporal modeling of audio-visual feature representations. Extensive experiments are conducted on the Voxceleb1 dataset to evaluate the proposed model. Results indicate that the proposed model shows promising improvement in fusion performance by adeptly capturing the intra-and inter-modal relationships across audio and visual modalities.