Consider the following:

We have two Nation States, A and B, with approximately equal nuclear arsenals (offensive and defensive capabilities).

Nation State B's intelligence apparatus determines a high probability that a new Artificial intelligence technology has been developed in Nation State A. They determine that this technology has the potential to dramatically undermine their own second strike capability. They believe this to be true with a high probability, although they are not 100% sure.

Nation State B is forced to choose one of two options. Given their limited information, they must decide quickly, as they have no way of ruling out the possibility that this technology isn't already deployed and ready.

One, they wait, and become sitting ducks in the hopes that Nation State A does not launch a first strike.

Two, they launch a preemptive strike, unprovoked. If the AI technology is truly capable of rendering their second strike capability useless, this is their only opportunity to launch a strike. Shoot em or lose em.

If Nation State B perceives an existential threat from Nation State A, it will have no choice but to launch an unprovoked nuclear strike.

Thus, the mere probability of a destabilizing AI technology leads to nuclear war.

Note the following details:
1. The AI doesn't need to ever actually be used
2. We don't even need to consider AGI. A task specific weak AI is more than sufficient.
3. The AI doesn't even actually need to exist, simply a convincing implied threat is enough to provoke war.
4. We don't require an ongoing war or conflict. We can consider this scenario in a peace time/cold war.
5. An on going conflict, even a proxy war or small scale conflict, simply further constricts Nation B to elect the preemptive strike.