South African ruling ANC leader Jacob Zuma backed a diplomatic push as the way to end political deadlock and rejected any suggestion of sending troops.
It said more than 20,580 people had been affected by cholera since August.
The cholera epidemic has added to pressure on President Robert Mugabe and Western countries have renewed calls on the veteran leader to step down.
Mugabe agreed to share power with opposition leader Morgan Tsvanigrai in September, raising hopes of a power-sharing government that could bring the country back from economic meltdown.
But negotiations are deadlocked over who should control key ministries.
Prominent figures, including Kenyan Prime Minister Raila Odinga and Nobel peace laureate and South African Archbishop Desmond Tutu, have called for Mugabe to go or for peacekeeping troops to be sent to Zimbabwe.
When asked in an interview with South Africa’s 702 Talk Radio whether he favoured sending troops to Zimbabwe, ANC leader Zuma said: "No. Why military intervention when there is no war? We should be pressurising them to see the light."
South Africa’s ANC-led government, however, has continued to back the regional SADC group’s efforts to mediate an end to the crisis. Former South African President Thabo Mbeki is leading the mediation of the power-sharing talks.