BEIRUT—A band of 48 Iranians being held hostage by Syria's rebel army journeyed from Tehran on a trip organized by a travel agency owned by the elite troops who support and protect the Iranian regime, people familiar with the trip said.

That connection—denied by Iran, a staunch supporter of the Assad government—suggests the hostages have strong ties to Iran's elite Revolutionary Guard Corps, as the rebels claim. Tehran, which says the hostages are religious pilgrims, warned...