Coca-Cola representatives said the adverts demonstrated their attitude to preserving cultural heritage.
The believers said the advertizing posters in Nizhny Novgorod showed the crosses on the domes of various well-known churches in the city, as well as views of the local Kremlin.
"Coca-Cola uses all these Orthodox symbols in a blasphemous way by placing images of Coca-Cola bottles inside the pictures," the letter complained to local prosecutors, the governor and the archbishop. "Some [church] images are deliberately turned upside down, including the crosses."
An inverted cross is one of the symbols of Satanism.
The Orthodox believers want the posters to be removed and Coca-Cola brought to trial for "inciting religious hatred and undermining national dignity."
Coca-Cola representatives said the company strictly complied with ethical norms and its adverts were an appeal to safeguard cultural monuments.
A spokesman for the bishop's office hailed the believers' letter. "It is important that such cases arouse reaction from ordinary people as well as priests."
Another case of the controversial marriage of fast-food and religion occurred in Britain in the mid-1990s, when the dome of St Paul's Cathedral in London was illuminated with an advert for Cadbury's chocolate bar "Wispa". The company was allowed to put up the advert after paying for restoration work to the cathedral's Whispering Gallery.