Companies, not governments, are at the cutting edge of developing new artificial intelligence (AI) technologies for military use, and regulation needs to keep pace with these advances. Yet geopolitical tension is undermining international cooperation on AI in the military domain. This paper examines opportunities for global cooperation to mitigate the risk of accidents and misuse of these technologies that could lead to escalation. Possible options include establishing an agreement to regulate autonomous systems, mandating human control over nuclear weapons and creating a UN-based institution to oversee responsible military applications of AI.