TOKYO—Japan and Southeast Asian nations signaled they are ready to work more closely together in the face of an increasingly assertive China, as their leaders met for a weekend summit in which concern about regional security was a major undercurrent.

But in a sign of the delicate balancing act that leaders face as they navigate the turbulent relationship between the region's two biggest powers, the gathering ended on Saturday with a joint statement that didn't mention China or its declaration of an air-defense identification...