They said the president has failed in his primary responsibility to protect lives.
The call comes in the wake of an attack on St. Ignatius Quasi Parish Ukpor-Mbalom in Ayar-Mbalom community of Gwer East local government area of Benue state on Tuesday, April 24, 2018, where suspected herdsmen killed two Catholic priests and 17 other worshipers.
In a communique signed by CBCN's president, Most Rev. Augustine Akubeze, and secretary, Most Rev. Camillus Umoh, on Thursday, April 26, 2018, the religious organisation argued that President Buhari has left Nigerians feeling exposed and vulnerable while faced with dark clouds of fear and anxiety.
The communique noted that the federal government has failed in its primary responsibility to protect lives with security agencies accused of deliberately turning a blind eye to the cries of helpless and harmless citizens.
CBCN also accused the president of failing to reconfigure the nation's security structure while deliberately placing security agencies "in the hands of the adherents of only one religion".
The statement read in part, "Since the President, who appointed the heads of the nation's security agencies has refused to caution them even in the face of the chaos and barbarity into which our country has been plunged, we are left with no choice but to conclude that they are acting a script that he approves of.
"If the President cannot keep our country safe, then he automatically loses the trust of the citizens.
"He should no longer continue to preside over the killing fields and mass graveyard that our country has become. Repeated calls from us and many other Nigerians on the President to take very drastic and urgent steps to reverse this ugly tragedy that threatens the foundation of our collective existence and unity as a nation have fallen on deaf ears.
"It is clear to the nation that he has failed in his primary duty of protecting the lives of the Nigerian citizens. Whether this failure is due to inability to perform or lack of political will, it is time for him to choose the part of honour and consider stepping aside to save the nation from total collapse."
The CBCN also urged the government to tread carefully on disarming Nigerians who legally procured weapons of self defence.
Suspected herdsmen have been involved in several attacks this year and have killed hundreds across the country, especially in the Middle Belt.