Recent advances in large multimodal models (LMMs) have recognized fine-grained grounding as an imperative factor of visual understanding and dialogue. However, the benefits of such representation in LMMs are limited to the natural image domain, and these models perform poorly for remote sensing (RS). The distinct overhead viewpoint, scale variation, and presence of small objects in high-resolution RS imagery present a unique challenge in region-level comprehension. Moreover, the development of the grounding conversation capability of LMMs within RS is hindered by the lack of granular, RS domain-specific grounded data. Addressing these limitations, we propose GeoPixel - the first end-to-end high-resolution RS-LMM that supports pixel-level grounding. This capability allows fine-grained visual perception by generating interleaved masks in conversation. GeoPixel supports up to 4K HD resolution in any aspect ratio, ideal for high-precision RS image analysis. To support the grounded conversation generation (GCG) in RS imagery, we curate a visually grounded dataset GeoPixelD through a semi-automated pipeline that utilizes set-of-marks prompting and spatial priors tailored for RS data to methodically control the data generation process. GeoPixel demonstrates superior performance in pixel-level comprehension, surpassing existing LMMs in both single-target and multi-target segmentation tasks. Our methodological ablation studies validate the effectiveness of each component in the overall architecture. Our code and data will be publicly released.