The two leaders held emergency talks in Pretoria as the release of the results of the vote — which has been postponed three times over the last two years — was further delayed.
Tensions have increased as international pressure mounts to publish the outcome in a country where past elections were marred by violence.
“The two presidents have called on CENI (Independent National Electoral Commission) to speedily finalise the vote tabulation and release the election results in order to maintain the credibility of elections,” South Africa’s foreign affairs ministry said.
The leaders “underscored that the delay in releasing the results of the elections can lead to suspicions and compromise peace and stability of the country”.
The CENI has blamed problems with collecting the data announced on Tuesday that provisional results of the much-delayed presidential election could be counted in “24 to 48 hours” after which an announcement will be scheduled.
South Africa, a non-permanent council member, is a leading power in the Southern African Development Community (SADC) that includes the DR Congo.
Lungu heads SADC’s section that deals with peace and security.
First results of the December 30 election to choose a successor to long-term President Joseph Kabila were due on Sunday.
Kabila was meant 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.
With international concerns growing over the peaceful transfer of power in sub-Saharan Africa’s largest nation, Western powers have upped the pressure.
Opposition presidential candidate Martin Fayulu earlier on Tuesday warned electoral authorities not to “disguise the truth of the polls” as he urged the authorities to publish the outcome.