Today, Kagame is president of Rwanda, and he insists on reconciliation between the warring groups.
CNN: From child refugee to Rwanda's reconciliation president
President Paul Kagame of Rwanda repeated this concern at a press conference this week.
BBC: US blocking UN report on DR Congo rebels, watchdog says
He said he had evidence implicating Rwanda's current President Paul Kagame, who has immunity from prosecution.
Mr Kagame blames the corruption and inefficiency of Congo's government for the county's eastern problems.
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RPF's leader, Paul Kagame, was elected president last month, with 95% of the vote.
Despite his ruthlessness Mr Kagame is regarded as a steadying hand in a chaotic region.
ECONOMIST: A leaked UN report looks very bad for Rwanda��s government
President Obama and President Kagame also discussed the longstanding governance problems in the DRC.
WHITEHOUSE: Readout of the President��s Call with President Kagame
The tiff is all the more baffling because Mr Museveni and Mr Kagame were once comrades-in-arms.
Some American officials are privately getting queasy about America's dogged backing for Mr Kagame.
ECONOMIST: Congo and Rwanda: Stop messing each other up | The
Paul Kagame (above), the president who has overseen all this, is a darling of the aid-giving world.
And the Americans may have to start thinking about making their loyalty to Mr Kagame more conditional.
ECONOMIST: Congo and Rwanda: Stop messing each other up | The
But Mr Kagame must reckon he has more to gain by removing him than by propping him up.
What is unclear is the extent of the relationship between the Rwandan president, Paul Kagame, with Mr Nkunda.
Jakaya Kikwete of Tanzania has nearly 50, 000 and Rwanda's Paul Kagame around 104, 000.
The PM said he would hold "firm" talks with Rwandan President Paul Kagame.
Mr Kagame's critics accuse him of leading a repressive regime, which jails opponents and cracks down on the media.
Mr Nkunda slipped into Rwanda last week still believing that his furtive friendship with Mr Kagame would protect him.
It will make uncomfortable reading for Mr Kagame's backers too, such as America and Britain, but little will change.
ECONOMIST: A leaked UN report looks very bad for Rwanda��s government
President Obama spoke today with President Kagame to discuss the situation in eastern Democratic Republic of the Congo (DRC).
WHITEHOUSE: Readout of the President��s Call with President Kagame
The startling improvement in Rwanda's business climate is largely thanks to Mr Kagame.
Mr Museveni and Mr Kagame have, in the past, quickly sorted out conflicts between their forces on the ground.
Mr Kagame says he has no ties except that they are both Tutsis.
Kagame that he hoped that Rwanda would continue its exemplary work in support of peace and security in the region.
Mr Kagame is sensitive to growing Western criticism of his increasingly autocratic ways, so he too may start looking east.
The West has long sought leaders, such as Mr Kagame, who can be relied on to spend aid money well.
Mr Kagame has hinted that some deputies have fallen short of the required standard and should be ejected by their parties.
Mr Kagame promises that he will step down from the presidency in 2017, in accordance with an admirable constitutional term limit.
Paul Kagame, Rwanda's vice-president and army chief, dismissed that report but said that many militiamen are being killed by the army.
In 1990, Kagame was attending a training course at Fort Leavenworth in the U.S. state of Kansas when Tutsi rebels invaded Rwanda.
CNN: From child refugee to Rwanda's reconciliation president
Meanwhile, Rwandan President Paul Kagame told the BBC that UN troops had "in some cases" made the situation in DR Congo worse.
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