About 6,000 Burundians have fled into Rwanda over the past month, Rwandan officials said, fearing violence in the build up to a presidential election.
Speculation has grown that Burundian President Pierre Nkurunziza will seek a third term, leading to the worst political tensions since a 12-year civil war ended in 2005.
Refugees at Rwanda's eastern Bugesera district, where most are housed, told Reuters last week that they fled fearing attacks from Imbonerakure, the youth wing of Burundi's ruling CNDD-FDD party, who, they say, harass and sometimes kill opposition members, an accusation the group denies.
Burundians started crossing the border in mid-March but numbers have swelled in recent days, data from Rwanda's ministry of refugee affairs showed. On Tuesday, 1,069 arrived, taking the total to 5,954.
Opposition parties and dissenting members within CNDD-FDD say Nkurunziza running for a third term would violate a 2000 deal that ended the conflict between Hutu and Tutsi ethnic groups. Nkurunziza, in power since 2005, has not yet stated he will run.
Opponents to a third Nkurunziza term said they planned to protest in the capital Bujumbura in coming days, after canceling a demonstration planned for Wednesday.
“The fight to persuade President Nkurunziza to abandon his intention to run for a third term continues,” said Jean Minani, chairman of FRODEBU-Nyakuri party, one of five main opposition groups. He called for a peaceful street protest.
The U.S. State Department on Tuesday advised its citizens to avoid political rallies, although it added that recent protests in Bujumbura have been largely peaceful.
Rwanda's President Paul Kagame has raised the issue of refugees and the risk of violence when he met Nkurunziza on Monday, the Rwandan presidency said in a statement.