Hundreds of people have held a demonstration in Goma, fearing persecution from government troops sent to eastern Deocratic Republic of Congo.
Residents of Goma fear they wil be targeted by Congolese soldiers
The Congolese Tutsis and Hutus share a similar ethnic background with the people of Rwanda.
The Congolese government is sending thousands of extra troops to the area, amid fears of a Rwandan invasion.
Rwanda has denied that its forces have entered DR Congo, though there have been reports of some attacks.
When the Congolese reinforcements come, "no Congolese Rwanda-speaker is going to be able to budge," said Dunia Bakarani, a spokesman for the Congolese Tutsi community.
Rwanda warned last week that it was prepared to send its troops across the border in search of Hutu rebels and former army troops, who fled after the 1994 genocide.
Rwanda invaded its much larger neighbour in 1996 and 1998, accusing successive Congolese governments of backing the Hutu rebels.
Separately, there were reports in the Ugandan press of clashes between Ugandan and Rwandan forces.
The Ugandan army has confirmed that a clash took place but said it is not clear whether it was with Rwandan forces or Congolese rebels, the BBC's Will Ross said.
Last week, President Joseph Kabila announced he would send some 10,000 troops to expel Rwandan forces from DR Congo.
"Rwanda has goals that are political, economic, exploitative and predatory," Mr Kabila said, in his first public reaction since reports emerged that Rwanda had sent troops into eastern DR Congo.
President Kabila cited aid workers' reports that "several thousand civilians have fled from zones where there is violence."
On Sunday, a spokesman for the UN mission in Congo told AFP that armed men suspected of being Rwandan soldiers have been attacking and burning villages for more than a week.
He said the UN had been unable to verify information independently because the region is difficult to access.
A UN spokeswoman in Goma, Jacqueline Chenard, said that a helicopter mission north of Goma had found only "phantom villages emptied of their inhabitants" and that inhabitants were fleeing because they were afraid of attack.
The BBC's Mark Doyle, who has just returned from the region, says that any Rwandan military action could unravel tentative moves towards peace throughout central Africa.
Last week, the UN Security Council urged Rwanda not to send troops into DR Congo but did not condemn Rwanda's action or impose sanctions on Mr Kagame, as the Congolese had wanted.
Rwanda withdrew its troops in 2002, under a regional deal to end five years of war in DR Congo, in which some three million people died.
Under the peace deal, the Hutu rebels were supposed to have been disarmed but progress has been slow.