Zuma asked the warring parties to refrain from violence as the East African Community continues to push for a peaceful end to the conflict.
"... the Peace and Security Council of the AU decided that all those whose action could jeopardise the inter-Burundian dialogue, including attacks by armed groups against government facilities and other targets, as well as refusal to respond to the invitation of the mediator shall be subjected to sanctions as provided for in the relevant decisions of [African Union] Council and other measures to be agreed upon," Zuma said.
Burundi's president Pierre Nkurunziza, however, skipped the talks.
Negotiations to end the violence in Burundi kicked off on Monday, this week at State House Entebbe in Uganda, with four former Burundian presidents attending the talks mediated by President Yoweri Museveni.
Ex-Presidents Pierre Buyoya, Sylvester Ntibantunganya, Domitien Ndayizeye and Jean Baptist Bagaza attended the inaugural session to draw the agenda for talks aimed at ending the bloody political unrest.
However, the talks seemed to be headed for a rocky route with the Burundi government side giving a condition that all "coup plotters should not be allowed to attend the negotiations".
The first deputy Chairperson of the ruling party, CNDD-FDD Victor Burikukikiye told the meeting attended by representatives of regional countries, international bodies and powers that it was "wrong to meet people who participated in the failed coup."
"Before we start the negotiations, there are things that must be addressed. Those who participated in the coup attempt should not participate," he said, adding that the talks' agenda must be agreeable and should reflect recent events in Burundi.
But, President Museveni told the warring parties not to give conditions before the negotiations begin.
Museveni also promised to send a team to Burundi to investigate the killings of civilians.
At least 240 have been killed since Burundi's crisis began in April, this year with more than 200,000 people having fled the country.
Violence was sparked by President Pierre Nkurunziza's controversial decision to run for a third term in office.
"I'm going to send a team privately as Uganda and as the chief mediator to investigate the reports of extra-judicial killings because that we shall not agree to," he said.
The president blamed sectarianism, which he described as "pseudo-ideology", indiscipline of armies, lack of vision by African leaders, and mismanagement of resources as the main causes of conflicts in Africa."Burundi had succeeded but along the way, it collapsed. The problem is clear. This pseudo- ideology has been a very big problem. It doesn't represent the interests of the people," he said.
The Burundian Minister of External Relations and International Cooperation, Alain-Aime Nyamitwe, who is the head of the government delegation accused the neighbouring Rwanda of recruiting rebels to fight the government of President Nkurunziza.
"For us to end this conflict, its better to be open and say what the problem is. There has been recruitment of Burundian refugees in Rwanda to distabilise Burundi," Nyamitwe said.
Rwanda President Paul Kagame during a press conference last week denied the accusations and asked whoever makes the claim to investigate.
"I think this is just childish," Kagame told a news conference in the Rwandan capital Kigali.
Leonard Nyangoma, the representative of Opposition also dismissed Nyamitwe's allegations about Rwanda training rebels to distabilise Burundi.
"The conflict in Burundi is fundamentally social, political and economic. We have a problem of militias, bad governance and insecurity," Nyangoma said.
The Opposition has been accusing Nkurunziza's government of deploying Imbonerakure, an armed militia to attack the Opposition.
Representatives of European Union, United States, UN Security Council, UN Secretary General, African Union, International Conference on the Great Lakes Region (ICGLR) and the East African Community attended the meeting at State House Entebbe.
The negotiations will resume on January 6 in Arusha, Tanzania.
The Opposition demands: Want deployment of an International peacekeeping force; amend 129 Article of the Constitution to allow political parties with less than 5 percent to have positions in government; end Corruption; equal distribution of resources; disarming and stopping Imbonerakure and ending political violence; government demands; no international peacekeeping force; coup plotters should not participate in the talks; investigate role of Rwanda in the conflict and end of political violence.