He was on the verge of making a comment but stopped, realizing it would be a mistake.
on the verge of (something)
Very closely approaching something; very nearly at the point at which something will happen. After weeks of failed experiments, I think we're finally on the verge of a breakthrough.
on the verge of
Close to, on the brink of, as in I was on the verge of calling the doctor when he suddenly got better, or Sara was on the verge of tears when she heard the news. This term uses verge in the sense of "the brink or border of something." [Mid-1800s]
on/to the verge of something/of doing something
at or close to the point or time when somebody does something or something happens: She was on the verge of tears.We’re on the verge of signing a new contract.