Joseph Kabila (pictured), who has led the African country since 2001, is thought to want a change in the constitution to enable him to stand for a third term in office.
Fr Léonard Santedi, Secretary General of the Catholic Bishops Conference in the DRC, said: "It is imperative that we respect the constitution, particularly regarding the number and duration of mandates of the president of the Republic."
There is concern such a constitutional change could delay elections scheduled for November this year, resulting in an escalation in political violence.
Father Santedi added: "Blocking the electoral process creates a worrying situation which risks plunging the country into chaos.
"The country is facing a deteriorating socio-economic and security situation, particularly in areas like eastern DRC. At this important moment, we urge political leaders to take action to ensure that violence and bloodshed are averted.
"We call on the international community to support the DRC in finding a lasting solution to the political situation, to back democratic electoral process, and support investigations into the recent massacres of communities in Beni and in the North Kivu region".
Despite it's vast mineral wealth the DRC is considered one of the world's poorest countries and it has been ravaged by a civil war spanning more than a decade, in which more than four million people have lost their lives.
Fergus Conmee, Head of Africa Programmes at the Catholic aid agency CAFOD, said: "The situation in the DRC is extremely precarious and the risk of political violence is extremely high.
"We support the Bishops' urgent call for peace and democracy at this time."