Violence broke-out in major cities on Tuesday one day after President Joseph Kabila refused to step down following the end of his second and final term in office, with no political transition or election in sight.
Chairman of the Episcopal Conference in the DRC (CENCO), Monsignor Marcel Utembi, said the organisation would like to see a deal reached "before Christmas".
Quoted by the AFP news agency, he added: "If the political and civil society actors do not reach a compromise by then... CENCO will draw the consequences."
Talks hosted by CENCO and attended by both ruling party and opposition figures broke up at the weekend without agreement.
But both sides have been urged by the United Nations - which has backed the CENCO-facilitated dialogue - to "work constructively and in good faith on the outstanding issues related to transitional arrangements leading to the elections."
Meanwhile, the UN estimates 19 people were killed and 45 hurt in clashes in the capital Kinshasa and the second city of Lubumbashi on Tuesday.
A deal reached between Kabila and small fringe opposition groups saw the President announce a new government overnight on Monday and an agreement he would remain in office until elections in April 2018.