The government and rebels reached a deal in principle in mid-2006 to halt two decades of violence that killed 300,000 people in the small central African nation of 8 million.
"The regional leadership asked us to convey the following message: that this programme is going to come to an end on the 31st of December," South African Defence Minister Charles Nqakula told reporters late on Thursday.
He was speaking after talks with President Pierre Nkurunziza and the Forces for National Liberation (FNL) rebel group.
Flanked by the foreign ministers of Tanzania and Uganda, Nqakula said the mediation team's mandate would not be extended into 2009. He urged both sides to complete the disarmament, demobilisation and reintegration of FNL combatants by then.
"It has been a very long process and we are not going to continue in a never-ending way to engage with a matter which is not the only game," he said.
"The Burundi matter is not the only programme leaders of the continent are dealing with, there are many other problems."
The FNL says it will only go through with implementation of the peace deal once it is accepted as a political party with the name "Palipehutu", which means party for the liberation of Hutus.
The government has rejected the demand, saying Burundi's constitution does not allow parties with ethnic affiliations.
(Reporting by Patrick Nduwimana) (For full Reuters Africa coverage and to have your say on the top issues, visit: http://africa.reuters.com/)
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