Cherished Pet Cremations has applied for permission to move into the vacant unit at 350 London Road which it said would be a 'low impact change' for the area.
The planning application proposes the formal change of use of the class of the building from storage to 'general industrial'.
But concerns have been raised about having a crematorium in a residential part of the city.
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'I find it shocking that this could be so close to my children's school and opposite a nursery,' a letter of objection from Alexandra Dawson, who lives nearby, says. 'It is a totally inappropriate use of this building.
'It is very disturbing to think that our air quality could also be affected by this. How can we be outside in our gardens with this next to us? I think that a much more suitable building could be found on an industrial estate.'
A statement submitted on behalf of the business, which is currently based in Meredith Road, says these facilities are needed close to where people live.
'As a pet loving nation, this business is an important service that is required in the heart of all urban communities and it is common to find such services within all main urban settlements to cope with the inevitable outcome of the general public owning animals, many of which have short life spans,' it says.
'The applicants propose to use state of the art high efficiency incineration equipment to burn small quantities, in a quiet and non-hazardous, discrete process.'
It adds that this use would also be less demanding in terms of parking than when the building was used for the storage of roofing equipment.
And the application has also drawn letters of support, welcoming the provision of a pet cremation service in North End.
Christina Thompson, who lives in Strode Road, said: 'This will benefit our area hugely, my previously animal passed away and I needed to travel for nearly an hour.
'Had something like this been on my doorstep I would have found thewhole situation a lot less stressful and less draining for my mental health.'
The application will be considered by Portsmouth City Council in the coming weeks.