The election's supervisors had faced mounting pressure at home and overseas to publish the results after repeated delays stoked fears for the giant country's stability.
The department of global relations and cooperation (Dirco) also said that the two presidents have agreed to monitor the situation in DRC and committed SADC's support and solidarity.
The presidents of South Africa and Zambia are urging Congo's electoral commission to "speedily" complete vote-counting and announce the delayed results of the December 30 presidential election.
Congo's electoral commission is meeting to discuss the results and could announce them as early as Wednesday.
The mineral-rich country has never had a peaceful transition of power since it gained independence from Belgium in 1960.
Congolese activist groups have urged people to "be ready to massively take to the streets" if the commission does not publish results in accordance with "the truth of the ballot boxes".
The son of major Congolese political figure Etienne Tshisekedi, the 55-year-old president-elect is the head of country's longtime main opposition party UDPS.
According to the initial timetable, after provisional results are released, definitive results are due on January 15 with the swearing-in of the new president three days later.
Anti-riot police have been deployed in the capital, Kinshasa, reports the BBC's Louise Dewast from the city.
Kabila was due to step down two years ago, but clung on to office, sparking widespread protests which were brutally repressed, killing dozens in a country that has been a battleground for two wars over the last two decades.
Their meeting came amid growing concern that unrest could erupt in DR Congo, following tightly contested presidential elections on 30 December.
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In a conference last week, the Church's bishops said that it knew the identity of the victor and demanded that CENI publish accurate results.
Candidates can appeal results if they wish and the final decision will be announced by the constitutional court.
South Africa and Zambia, DRC's neighbour to the south, joined the clamour to publish the results.
The bloodshed revived traumatic memories of the DRC's brutal past. He was elected in 2006, and secured another term in controversial elections in 2011.
While Nshole acknowledged the difficulties in manually counting votes, especially in remote areas, he warned that the longer the election results are delayed, the more that suspicion will grow among the Congolese people.
"There's no spirit of revenge", said Tshisekedi.
Talk of a possible rapprochement between the UDPS and Kabila was also fuelled after Tshisekedi told Belgian newspaper Le Soir the president could be honoured for his behaviour after stepping down. Tshisekedi's party on Tuesday called him the "presumed winner" and indicated that he has had contact with Kabila "to prepare a peaceful and civilized transfer of power".
DRC is choosing a successor to the departing President Joseph Kabila, who has ruled since 2001.
How will Congolese citizens react?. He will do what he wants.
Fayulu is backed by former Katanga governor Moise Katumbi, considered a "Judas" by Kabila, and ex-warlord and former vice president Jean-Pierre Bemba. The keyword for us is: "There's no revenge".
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