Mired in poverty but rich in minerals, the former French colony has been battered by a conflict between rival militias that began in 2013 after then president Francois Bozize was overthrown.
The bishops made the appeal during an episcopal conference in the capital Bangui on Sunday.
"In the name of God, we ask the armed groups to unconditionally lay down their arms," and "stop all sorts of crimes (including) looting natural resources and causing the dysfunction of the state", they said during mass.
The closing ceremony of the conference was attended by President Faustin-Archange Touadera.
The bishops also condemned the delay in disarming fighters from varied groups and "the slow response and inaction by some contingents of MINUSCA", the UN peacekeeping force in the country.
Thousands of people have been killed in the fighting. According to the UN, more than a million people have fled their homes and 2.4 million people -- more than half of the Central African population -- are in need of humanitarian aid.
The country has seen an upsurge in violence since France shut down its Sangaris mission there last year, but the UN Security Council agreed in November to extend its MINUSCA peacekeeping mission for a year and beef it up with 900 extra troops.
The bishops called for the speedy deployment of government troops although they noted that the soldiers, like the various rebel groups, turned to extortion to supplement their income.
The army's restructuring has been hobbled by a UN arms embargo in place since 2013. However, the UN authorized Russia last month to deliver weapons to CAR and China got the go-ahead in October to supply military equipment.