Mr Nkurunziza survived an attempt to topple him last month
Burundi's National Assembly Speaker Pie Ntavyohanyuma is reported to have fled to Belgium, adding to a growing list of critics of President Pierre Nkurunziza who have gone into exile.
He holds Belgian citizenship, as does second Vice-President Gervais Rufyikiri who fled to Belgium on Wednesday, saying he feared for his life.
Both have been critical of Mr Nkurunziza's decision to run for a third term in presidential elections due next month.
Meanwhile, anonymous pamphlets are circulating in Burundi's capital, Bujumbura, warning people against voting in Monday's parliamentary poll.