According to Vatican Radio Archbishop Evariste Ngoyagoye, the Metropolitan Archbishop of Bujumbura, said in a statement: "We call upon politicians in power not to speculate or misinterpret the constitution. All the constitution provisions about the President's terms are very clear: no President can lead the country more than two terms of five years each".
The Southeast African state is caught in a dispute on whether President Pierre Nkurunziza, who has been in power since 2005, should be allowed to run for another term given that the former rebel leader was selected by lawmakers rather than voted into office in 2005 for his first term.
Under the constitution, he is allowed to serve only two terms but his supporters argue his first term should not count.
President Nkurunziza himself has not yet said that he will run, although his supporters affirm he can.
The Archbishop's comments mark the first time the Catholic Church has taken a position officially on the debate about a third term for President Nkurunziza. The Church played a key role in peace talks in Burundi.
Catholics in Burundi represent about 70% of the total population.