"We're working together to realise the vision of a free, democratic and prosperous Zimbabwe," Mrs Clinton said in a joint news conference with South African International Relations Minister Maite Nkoana-Mashabane.
"We're going to be closely consulting as to how best to deal with what is a very difficult situation for South Africa and for the United States, but mostly for the people of Zimbabwe."
Zimbabwe's economy has improved in recent months but the US is concerned that many of the political and social reforms promised by President Robert Mugabe following the power-sharing agreement with Prime Minister Morgan Tsvangirai have not yet been implemented.
In their meeting on Saturday, Mrs Clinton is expected to ask Mr Zuma to use his influence to combat what she has called "negative effects" of Zimbabwean President Robert Mugabe. Earlier, Ms Nkoana-Mashabane she believed the Obama administration would work alongside the African Union in helping to bring peace to parts of Africa.
"We see this administration and the government of the USA as a strategic partner on the political front, as we work with them to look at the mechanisms to resolve areas of conflict working together with the African Union," she said.
Mrs Clinton is also scheduled to meet Deputy President Kgalema Motlanthe.
She will also attend a conference with Health Minister Aaron Motsoaledi before attending National Women's Day events in the capital, Pretoria.
Relations between the US and South Africa were warm during the 1990s under Presidents Mandela and Bill Clinton, says the BBC's Jonah Fisher in Johannesburg.
A commission was established to prioritise areas of co-operation but when Mr Clinton left the White House this was quietly forgotten.
South African officials hope that the visit by Mrs Clinton, the former US president's wife, will signal a new period of co-operation to support the already strong business links, says our correspondent.
Hillary Clinton spoke about Somalia at the University of Nairobi
Mrs Clinton began her seven-nation African tour in Kenya on Wednesday where she held talks in Nairobi with Kenya's president and prime minister.
Addressing African leaders at an economic summit, Mrs Clinton said the continent had "enormous potential for progress".
But she stressed that harnessing that potential would require democracy and good governance.
Before Mrs Clinton arrived in Kenya, the US embassy in Nairobi had issued a statement scolding Kenya for its decision not to set up a local court to seek justice for the victims of the deadly clashes which followed the 2007 election.
On Thursday, Mrs Clinton met the Somali President Sheikh Sharif Sheikh Ahmed in the Kenyan capital.
She offered to increase US support for his unity government and to "take action" against neighbouring Eritrea if it does not stop supporting militants in Somalia.
Eritrea denies supporting Somalia's al-Shabab militants, who are trying to overthrow Somalia's government.
The Eritrean Information Minister Ali Abdu told the BBC Mrs Clinton's comments were "very disappointing" and that the White House had "failed to learn mistakes of the previous US administration".
Mrs Clinton's 11-day trip will take her to Angola on Sunday before she heads to Nigeria, Liberia, the Democratic Republic of Congo and Cape Verde.
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