"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.
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.
"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."
