Six of Burundi's pro-Tutsi parties have walked out a meeting with chief peace mediator, South Africa's Deputy President Jacob Zuma.
Jacob Zuma has played a leading role in Burundi's peace process
Mr Zuma was in Burundi to brief parties about a draft power-sharing agreement reached last week in South Africa.
The proposal suggests the national assembly and government be composed of 60% ethnic Hutus and 40% Tutsis.
Meanwhile, the main Hutu rebel group has said it will rejoin the power-sharing government it left in May.
The FDD says it has now been granted all the posts it was promised under a ceasefire deal agreed last year.
Mr Zuma is trying to mediate a comprehensive peace deal but the Tutsi parties say the proposals only reflects the views of Hutus, who account for 85% of Burundi's population.
"We decided to withdraw because Mr Zuma refused to listen to us... he refused to be the mediator he ought to be," a spokesman for the main Tutsi party Uprona told the AFP news agency.
Uprona, previously Burundi's ruling party, wants representation to be based on party affiliation, as well as ethnicity, fearing that otherwise Hutu parties could field Tutsi candidates.
The six parties asked to meet Mr Zuma privately to discuss their objections to the South African-brokered proposals for the new constitution.
But Mr Zuma refused, explaining he was only in the capital, Bujumbura, to brief the signatories of the Arusha peace accord, which was supposed to end 11 years of civil war.
Hutu rebels are being integrated into the Tutsi-dominated army
According to the BBC's Prime Ndikumagenge in Bujumbura, Mr Zuma is now likely to brief regional heads of state about the deadlock, who will then put pressure on the different parties to reach a resolution.
Our correspondent says there is concern that deadlock at the political level might affect the military process.
Ceasefire agreements are holding and the process of integrating the Tutsi-dominated military with Hutu rebels is continuing, he says.
Under the terms of the peace accord elections are due by the end of October when the new constitution has to be passed by parliament and a referendum.
Some 300,000 people have been killed since the civil war broke out in 1993.
About 5,000 United Nations peacekeepers are in the country to support the peace process.