Accorsi, whose tenure had seen the country climb more than 100 places in the FIFA rankings, said in a radio interview: "My last salary was in September.
"I had been hoping after talking to senior people in the government that the problem would be sorted out even if they paid a portion but they have not responded. I have finally decided to leave but with much regret."
The Central African Republic host Botswana on June 2 and then play in Ethiopia the following weekend in their opening World Cup qualifiers. South Africa are the other team in their group.
The Central African Republic also play two matches against Egypt in the African Nations Cup qualifiers later in June.