Tsvangirai and Mugabe remain deadlocked over crucial appointments, including the head of the central bank and the attorney-general.
"The remaining issues are not insurmountable and can be overcome," Zuma said at the dinner.
"The most difficult part has been travelled."
Mugabe sought to downplay his differences with Tsvangirai, calling their disputes "teething problems".
"I am happy to inform you that the inclusive government is alive and well," Mugabe told Zuma at the dinner.
"Indeed, a political accommodation of this nature is bound to experience teething problems."

'Punitive measures'

Mugabe, 85, in power since independence nearly three decades ago, again insisted the main problem facing the government was Western sanctions against him and his inner circle.

"Those countries who have hitherto imposed sanctions on us still maintain these illegal punitive measures inspite of progress we have made as an inclusive government," Mugabe said.
"We have made progress since the formation of the inclusive government," he said.

"Inflation has been tamed and schools and hospitals are functioning. Our greatest factor is sanctions."
The sanctions include a travel ban and a freeze on bank accounts  in the European Union and US.
Zuma was also set to address the Harare Agricultural Show, the country's biggest farm trade fair.