They published a statement after hearing councillors had passed a motion to ask the Home Secretary to remove the city as an area which welcome asylum seekers.
'Cluster areas' is the name given to towns and cities which agree to help cut the burden on London when it comes to housing people coming into the UK.
The motion stated: "This council acknowledges the chaotic and dangerous conditions that exist for civilians in Syria and elsewhere.
"It supports efforts by the government to provide aid to those displaced by violence. However it is concerned that any addition to the number of asylum seekers housed in the city will put an undue strain on already stretched local services. It therefore asks the Chief Executive to write to the Home Secretary requesting that Portsmouth be removed from the list of cluster areas."
In response, clergy at the Cathedral said: "[The council's] rejection of asylum seekers is mean spirited and narrow minded.
"The Cathedral has generous hospitality as one of its core values, and we are proud that this trident has always applied to the whole City. "
Speaking on Premier's News Hour, Canon Peter Leonard went further stating: "We're an important maritime place with people passing through.
"We've always been welcoming and open to people in need, particularly asylum seekers, so this flies in the face of that."
Councillors have defended the decision claiming it will ease the pressure on school places, children's services, social care.
When asked by Premier to the Cathedral's comments, the Council refused to comment.
Premier's Antony Bushfield speaking to Canon Peter Leonard: