JOHANNESBURG—According to witnesses and a senior U.S. official, a Russian merchant ship whose owner has allegedly transported weaponry for the Kremlin turned off its transponder last month before covertly docking at South Africa's main naval facility, where it delivered and loaded undisclosed commodities.

When asked what the ship was carrying or what had been placed aboard it at the Simon's Town navy base, South Africa refuses to comment. In response to American worries, the country's military minister dismissed them, claiming that Washington "threatens Africa, not just South Africa, of having anything that is even smelling of Russia."