The game sees a shoot-out take place in the cathedral's nave
The Church says Sony did not obtain permission to use the interior in the war game Resistance: Fall of Man.
The game, which has sold more than one million copies, shows a virtual shoot-out in the cathedral's nave in which hundreds of enemies are killed.
Sony said it believed it had sought all necessary permission for the game.
'Not reality'
The company said in a statement: "Sony Computer Entertainment Europe is aware of the concerns expressed by the Bishop of Manchester and the cathedral authorities... and we naturally take the concerns very seriously.
We believe we have sought and received all permissions necessary for the creation of the game
Sony Computer Entertainment Europe
Fantasy meets reality
"Resistance: Fall of Man is a fantasy science fiction game and is not based on reality.
"We believe we have sought and received all permissions necessary for the creation of the game."
The firm said it would be contacting the cathedral authorities on Monday "to understand their concerns in more detail".
But the Church said Sony did not ask for permission to use the cathedral and has demanded an apology and the removal of the game from shop shelves - otherwise it will consider legal action.
Sony said the game was not based on reality
The Bishop of Manchester, the Right Reverend Nigel McCulloch, described the decision to feature the city's cathedral as "highly irresponsible" - especially in the light of Manchester's history of gun crime.
"It is well known that Manchester has a gun crime problem," he said.
"For a global manufacturer to re-create one of our great cathedrals with photo-realistic quality and then encourage people to have guns battles in the building is beyond belief and highly irresponsible.
We are shocked to see a place of learning, prayer and heritage being presented to the youth market as a location where guns can be fired
Rogers Govender,
Dean of Manchester Cathedral
"Here in Manchester we do all we can to support communities through our parish clergy. We know the reality of gun crime and the devastating effects it can have on lives. It is not a trivial matter."
The Dean of Manchester Cathedral, the Very Reverend Rogers Govender, added the game was "undermining" the work of the church.
"We are shocked to see a place of learning, prayer and heritage being presented to the youth market as a location where guns can be fired.
"This is an important issue. For many young people these games offer a different sort of reality and seeing guns in Manchester Cathedral is not the sort of connection we want to make.
"Every year we invite hundreds of teenagers to come and see the cathedral and it is a shame to have Sony undermining our work."
'Mythical'
Patsy McKie, from Mothers Against Violence, whose son Dorrie was killed in Manchester, said it was time to stand up to the makers of violent games.
"I believe it's something that needs to be taken seriously first by the Church but also by parents.
"There's a war going on - not just in Iraq, but right here on our doorstep."
Sony described the game as being set "in an alternate and mythical version of Europe in the 1950s, in which the enemy are strange-looking alien invaders seeking to destroy humanity".
Earlier, David Wilson, a Sony spokesman, told The Times newspaper: "It is game-created footage, it is not video or photography.
"It is entertainment, like Doctor Who or any other science fiction. It is not based on reality at all. Throughout the whole process we have sought permission where necessary."
Katedra w Manchesterze
Angielski Kościół grozi wszczęciem postępowania przeciwko Sony Entertainment za umieszczenie katedry Manchesteru w tytule startowym konsoli PlayStation 3, ''Resistance: Fall of Man''. Gra, której akcja toczy się w alternatywnej historii m.in. w Manchesterze zawiera strzelaninę, która dzieje się w murach katedry.

Scena zawiera grupkę ludzi (w tym gracza), próbujących ochronić się przed atakującymi ich Chimerami - nowej, niebezpiecznej rasy ludzkiej.

Kościół zażądał przeprosin, mówiąc, że Sony nie pytało o pozwolenie na umieszczenie katedry w grze, dodatkowo opisując grę jako "chorą i świętokradczą".

Rzecznik Sony bronił gry, mówiąc w wywiadzie dla Daily Telegraph, że "gra w ogóle nie bazuje na rzeczywistym świecie" i porównując ją do serii ''Doctor Who''.

Kościół wyśle list z prośbą o przeprosiny i wycofanie gry ze sprzedaży do Sony w poniedziałek.