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The result will see Mugabe, 89, who has ruled Zimbabwe since independence in 1980, remain in office for the next five years.
President Zuma has reiterated South Africa’s readiness to continue to partner with Zimbabwe “in pursuit of a mutually beneficial cooperation”, said a statement from the president’s office.
South Africa is Zimbabwe’s biggest trading partner.
According to official figures, trade between Zimbabwe and South Africa amounted to about $5.9 billion last year.
The Southern African Development Community (SADC) ratified last week’s polls as free and peaceful.
“This election was free and very, very peaceful,” said Bernard Membe, Chief of the SADC mission overseeing the Zimbabwe elections.
The African Union (AU) observer mission in Zimbabwe also declared that the presidential elections were “free, honest and credible”.
However, both the AU and the SADC said they would wait for further information before giving a final verdict.
Meanwhile, the Federation of Unions of South Africa (FEDUSA) said on Monday that the polls in Zimbabwe were “not fair”.
“Firstly we must agree that the Zimbabwean elections of 2013 were peaceful and without obvious intimidation, especially in light of what happened in 2008. However, we can categorically state that the electoral processes were not fair,” said a statement from the union body.
FEDUSA had in April cautioned the Robert Mugabe government to recognise trade unions in Zimbabwe after police broke up a meeting of the Zimbabwean Trade Unions in Harare.
Western observers were barred from the recent elections meaning the AU and SADC were the crucial poll watchers.
The reaction from the United States and the United Kingdom differs greatly from that of the AU and SADC.
US Secretary of State John Kerry said on Saturday that “the United States does not believe that the results announced…represent a credible expression of the will of the Zimbabwean people”.
Britain’s Foreign Minister William Hague echoed the US position when he said that there are serious questions regarding “the credibility of the election”.
Mugabe’s main rival, Movement for Democratic Change (MDC) leader Morgan Tsvangirai termed it “a stolen election”, amid allegations of electoral irregularities.
With inputs from Agencies