We present Meerkat, an audio-visual LLM equipped with a fine-grained understanding of image and audio both spatially and temporally. With a new modality alignment module based on optimal transport and a cross-attention module that enforces audio-visual consistency, Meerkat can tackle challenging tasks such as audio referred image grounding, image guided audio temporal localization, and audio-visual fact-checking. Moreover, we carefully curate a large dataset AVFIT that comprises 3M instruction tuning samples collected from open-source datasets, and introduce MeerkatBench that unifies five challenging audio-visual tasks.