More than 1,000 refugees a day are arriving in Burundi from the Democratic Republic of Congo, officials say.
More than 30,000 people have fled the recent fighting, say officials
The refugees fear renewed fighting after government forces took back the eastern Congolese town of Bukavu from renegade soldiers earlier this month.
The mayor of Rugombo in Burundi, Onesphore Nduwinmana, said more than 30,000 people had crossed into the country to escape the recent fighting.
Kinshasa is trying to re-establish control after a five-year civil war.
Most of the first refugees to arrive were from the same Congolese Tutsi ethnic group as the rebels who fear reprisals from government soldiers.
However, people from other tribes have also started arriving.
"I do not know who was shooting or who has control of the area but there was a heavy exchange of gunfire," said refugee Maze Kahindo, who arrived in Burundi on Saturday.
"I ran from the field with my wife and child."
The refugees are seeking shelter at two sites in Cibitoke province.
The rebel General Laurent Nkunda who headed the brief take-over of Bukavu said he would not engage in further fighting because his demands had been met.
The United Nations has dismissed his claims to be preventing a genocide.
Gen Nkunda had said that his fellow ethnic Banyamulenges were being targeted and killed by the army.
But the head of a team of UN investigators could only confirm the death of four Banyamulenge civilians in recent clashes.