MOSCOW—Russian special-operations forces have played a pivotal part in the Syrian ground offensive to retake Aleppo, a role shielded by secrecy about their operations there.

In the wake of Russia’s punishing aerial bombardment, Russian special forces have been operating in Aleppo for almost two months, helping the Syrian army with a focus on targeting rebel leaders in the eastern half of the city, according to two experts on Russia’s military. On Sunday, the weekly state news program Vesti Nedeli offered a rare glimpse of...