Bishops from the Church have restated their stance against any constitutional amendments that would open the way for President Kabila to sit for a third term.
President Joseph Kabila
Took to power January 2001
Succeeded his father Laurent-Desire Kabila
His term expires in 2016.
The constitution in DRC only allows for two terms to be served by a president, with each term lasting five years.
The Catholic Information Service for Africa says that President Joseph Kabila wants to hold a "national dialogue" to make sure that "peaceful elections" go ahead, however the opposition think this is so that he can bypass the constitution.
Bishop Nicolas Djomo of the Catholic Diocese of Tshumbe, and the President of the National Episcopal Conference of Congo, said: "Dialogue is the path and peaceful solution to the crisis.
"It is a constituent element of any democratic system.
"We need to emphasize that dialogue must take place in full respect of the constitutional and institutional framework in force.
"To do otherwise would result in danger, with incalculable consequences for the nation."
President Kabila took office in 2001 after his father during the Second Congo War, which lasted until 2003. His father overthrew the previous president.
No date has been given for the 2016 elections yet.