Thousands of people are leaving - fearing ethnic clashes
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Some 17,000 refugees have streamed into northern Burundi from the Democratic Republic of Congo since clashes earlier this month.
"More refugees are expected, given the situation is so unstable," said the UNHCR's Jennifer Pagonis.
A dissident general threatened to resume attacks on Tuesday and warned new government troop movements could plunge the area into fresh conflict.
The fleeing civilians say they are terrified of renewed fighting.
The Congolese government has accused Rwanda of massing troops on its border and dismissed General Laurent Nkunda's ultimatum, urging him to surrender instead.
DR Congo's Foreign Minister Antoine Ghonda told the BBC that troops loyal to General Nkunda had committed crimes including looting and rape and should be brought to justice.
Tensions
Rwanda rejects allegations by the DR Congo that it has deployed extra troops along the border between the two countries.
A statement from the Congolese army also described General Nkunda, whose troops occupied the town of Bukavu earlier this month, as a spokesman for the Rwandan army.
But speaking to the BBC's Focus on Africa, Rwandan Foreign Minister Charles Muligande refused to condemn the dissident general's actions, describing them as an internal matter for DR Congo.
Rwanda also denies Congolese claims that it was behind the week-long takeover of Bukavu.
UN spokesman Sebastian Lapierre attempted to play down concerns saying there was no need to worry unless the Rwandan troops crossed the border.
Weeks of insecurity between government loyalists and General Nkunda's rebels are proving the most serious threat to DR Congo's fragile peace process aimed at ending years of conflict in central Africa.
On Monday, UN relief coordinator Jan Egeland warned that the humanitarian situation was acute in eastern DR Congo, with 3.3m people cut off from aid.
Clashes
The United Nations is also investigating reports of further fighting north of Uvira.
Renegade soldiers expelled from Bukavu last week are believed to be involved in clashes with government militia.
According to General Nkunda he went to Bukavu to protect civilians, in particular the Banyamulenge ethnic group, who he claims were being attacked.
The UN has 10,800 troops in DR Congo - although those sent to Bukavu did not stop the town falling to the rebels.