The demonstrations highlight the souring of relations between the Central African neighbors since Burundi President Pierre Nkurunziza was re-elected for a disputed third term.
Burundi was rocked by violent street protests for months after Nkurunziza's April announcement that he would seek another term.
At least 400 people have died since then in violent street protests, assassinations, attacks by a rebel group and a failed coup attempt. More than 200,000 Burundians have fled to neighboring countries, mostly to Rwanda. Burundi is accusing Rwanda of training and arming rebels in the refugee population.
Burundi's Interior Minister Pascal Barandagiye, in a radio broadcast urging people to participate in the demonstrations, accused the Rwandan government of trying to topple Burundi's government through military means.
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Demonstrators camped at Rwanda's embassy in Bujumbura today, singing songs against Rwanda President Paul Kagame.
The songs described Kagame as an enemy whom Burundians are going to "kumesa." The Kirundi word kumesa means wash. During Burundi's civil war a decade ago, "to wash someone up" was a euphemism for killing people perceived to be enemies.