The US government told a federal judge on Friday that its new policy dealing with transgender individuals in the military doesn’t discriminate against them as a class.

The Department of Defense instead told Judge Ana C. Reyes of the US District Court for the District of Columbia that the policy deals with gender dysphoria, which is a medical condition. Gender dysphoria is a subset of being transgender, and is the distress a person feels when they’re uncomfortable in their sex at birth.

That assertion was made in papers filed Friday ahead of a hearing at which the US sought to ...