The parties include Mugabe’s Zanu-PF, the Movement for Democratic Change (MDC) headed by Tsvangirai and an MDC splinter group led by Arthur Mutambara.
Frequent wrangling over policy and the slow pace of reforms have held back progress in the unity government.
Among the issues that have divided the parties is the appointment of the central bank governor and the attorney-general.
Last October, Tsvangirai boycotted cabinet meetings for three weeks, saying he would only take part if disputes over key posts and a crackdown against his supporters were settled.
The standoff was later resolved by the Southern African Development Community (Sadc) regional leaders at a special summit in Mozambique.
Zuma was tasked with helping the parties resolve their differences.
Al Jazeera’s Haru Mutasa, reporting from Harare, the Zimbabwean capital, said Zuma was not likely to suggest any practical solutions to the political problems.
“It’s unlikely that Zuma will actually come up with any solution to Zimbabwe’s problems, but he’ll have some idea about how serious these problems actually are,” she said.
“Then from there he’ll address the regional body, Sadc, and maybe a way forward on how to handle Zimbabwe’s political deadlock.”
She said that some analysts in South Africa were saying that the visit could be a chance for the president to make himself look good.
“Right now, in South Africa, he is not very popular with his people. People are protesting over service delivery, over lack of running water, over electricity and it seems the president needs to kind of boost his image, so to speak,” she said.
“And if he scores something in Zimbabwe, it could actually go towards helping his needs at home.”
The South African president’s visit comes only a week after Britain, Zimbabwe’s former colonial ruler, rebuffed his calls for an end to EU sanctions on Mugabe and his allies.
Zuma said he disagreed with the view expressed from outside Zimbabwe that more pressure in the form of sanctions was the way forward.