“It is necessary that the real actors in the conflict, fighting for power, sit together immediately,” the statement said, read out on Catholic radio by Bishop Gervais Bashimiyubusa, as well as in churches across the country.
President Pierre Nkurunziza won a highly controversial third term in July in polls boycotted by the opposition and denounced by the United Nations as neither free nor fair.
His re-election bid sparked an attempted coup by rebel generals and months of civil unrest led by opposition groups, who condemned it as unconstitutional.
Bashimiyubusa warned against those who may be tempted to “take the path of war.”
The Catholic Church, followed by some 60% of the country, has previously spoken out against the president, saying his third-term went against a peace deal that helped end the 1993-2006 civil war, when at least 300 000 people were killed.
The Church message said the situation in the capital Bujumbura was “very worrying”, and warned people had been “brutally murdered”, as well as others who had been kidnapped, tortured or imprisoned without trial.
Many have raised alarm bells at the risk of renewed conflict in Burundi, which lies in the heart of central Africa’s troubled Great Lakes region.
Burundi’s constitution only allows a president to be elected twice – for a total of 10 years in power.
But Nkurunziza argued ahead of the poll that he had only been directly elected by the people once. In power since 2005, when he was selected by parliament, he was first re-elected in 2010.