“The government and the people of South Africa share the grief of the entire Royal Family as well as the government and people of the Kingdom of Saudi Arabia at this time of bereavement,” Zuma said in a statement.
“South Africa lauds King Abdullah for his leadership role and efforts as a peace-maker and mediator, particularly in the Middle East region.”
Zuma said relations between the two countries were cordial, and that they had been formalised in November 1994 during a visit by then president Nelson Mandela to the country.
According to Deutsche Presse-Agentur (DPA), King Abdullah, 91, was laid to rest on Friday in the city of Riyadh.
He had been in hospital for several weeks suffering from a lung infection.
He had been on the throne since 2005, DPA reported.
Abdullah’s half-brother, Crown Prince Salman, is the new king.