Comparative genomics and synthetic biology require models that can interpret, annotate, and design DNA sequences across species, yet genomic models have not combined these capabilities beyond a few well-characterized organisms. Here we introduce Nucleotide Transformer v3 (NTv3), a long-context cross-kingdom foundation model that provides a common backbone for functional prediction, gene annotation and controllable sequence generation across phylogenetically diverse species. NTv3 is pretrained on more than 128,000 genomes using sequences up to 1 Mb and post-trained on 16,262 functional tracks across 15 animal and plant genomes. NTv3 performs comparably to AlphaGenome on matched human assays and matches or exceeds evaluated published models for functional-track prediction across 19 species spanning mammals, birds, fish, plants, fungi and protists. Ablation experiments show that both genome pre-training and expanding functional supervision from human and mouse to 15 species improve track prediction. Leveraging these learned functional representations, NTv3 outperforms leading ab initio gene predictors across mammals, plants and insects, with fewer spurious gene models and improved recovery and reduced fragmentation of long genes. Finally, the same representations can be used with discrete diffusion to design regulatory DNA sequences with specific activity levels. We demonstrate this in plant and fly promoters and enhancers, and experimentally validate the activity and promoter selectivity of the generated fly enhancers. Together, NTv3 unifies genome interpretation, gene annotation and regulatory sequence design across the animal and plant kingdoms, with direct relevance to agriculture, biodiversity research and biotechnology.