The pair, whose names were not disclosed, were kidnapped in Yemen's central province of Taiz on Monday by unknown gunmen in front of a hotel in the town of Howban, about 250km south of the capital Sana'a.
The pair, who were involved in the development of the hotel, were reportedly in a dispute between developers and the landlord shortly before the abduction.
Five people have been arrested in connection to the kidnapping, although the whereabouts of the pair are still unknown.
The department said the engagements seeking to secure their release are on-going. South Africa's ambassador to Saudi Arabia arrived in Yemen on Wednesday to engage on the matter and establish the facts that led to the kidnapping.
This is the latest kidnapping involving foreigners in Yemen, where al-Qaeda militants or tribesmen often kidnap foreigners for ransoms. Most kidnapped foreigners are released unharmed after ransoms are paid.
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