But the Tutsis want the presidency and vice presidency to alternate between the two communities.
Despite being in the minority, the Tutsis have dominated politics and the army since independence.
Fearing reprisal, thousands of Congolese Tutsis have fled across the nearby border into Tutsi-run Rwanda.
In the new Rwanda you will have Tutsis voting for Hutus and vice versa.
One of his main problems is that many of his men are Tutsis from eastern Zaire.
In Rwanda in 1994, the world watched while the Hutu majority slaughtered some 700, 000 Tutsis.
To stop them, Rwandan Tutsis recruited Kabila, an ageing revolutionary, and engineered his rise.
Soon hundreds of fellow Tutsis in the Congolese army were deserting and joining him.
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Its cocktail of Congolese Tutsis, exiled academics and old-style Mobutu supporters became increasingly fractious.
They attack both Hutus and Tutsis, but Tutsis, being in the ascendant, are their main target.
Nkunda says his forces are fighting to defend Congolese Tutsis from Hutu militants who escaped to Congo.
However, Burundi's Tutsis would fear for their own safety if the nation's army was commanded by Hutus.
But power lies with the Tutsis, who are doing little to heal the wounds or mend the fabric.
It was sparked by lingering tensions over the 1994 slaughter of ethnic Tutsis by majority Hutus in neighboring Rwanda.
The soldiers, mostly Tutsis, became part of the national army through that accord.
Most of the 800, 000 people killed were ethnic Tutsis but Hutu moderates were also slaughtered by the Hutu extremists.
Mr Kagame says he has no ties except that they are both Tutsis.
Tutsis ruled the country from independence in 1962 until they unexpectedly lost political power in a 1993 multi-party election.
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The Rwandan government and the Tutsis in Congo are, they say, his pawns.
At the time, Nkunda said his forces were fighting to defend Congolese Tutsis from Hutu militants who escaped to Congo.
The Tutsis of eastern Congo, though they were living there before the borders were drawn, have never been given citizenship.
On April 6, 1994, a missile shot down the plane carrying president Habyarimana, officially starting the ethnic cleansing of Tutsis.
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Despite its past as a Hutu rebel group, the movement claims to have rapidly recruited Tutsis since becoming a political party.
Though Tutsis account for only a small proportion of Rwanda's population, the most powerful people in the government are all Tutsi.
Much of the rhetoric on radio and television was racial, designed to turn opinion against the Tutsis supposedly behind the rebellion.
But the rebel groups still fighting say that while Tutsis dominate the army, a Hutu president would be mere window dressing.
But the Hutus' three-month slaughter of Tutsis left more than 800, 000 dead.
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Some moderates from the Hutu majority who supported Tutsis were also killed.
In the east, ethnic groups such as the Babembe and the Bahunde resent the increasing dominance of the Tutsis, Zairean and Rwandan.
Rwandan Tutsis take Congolese charcoal, timber and minerals for sale in Rwanda.
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