Friends of Victoria Park said the University of Portsmouth proposals would lead to harm the city 'could not afford'. Their concerns have been backed by city council officers.
But the university's vice chancellor said the £100m building had been designed to 'complement' the park and that it would be an 'asset' for the city.
The application, submitted last month, proposes the construction of a new academic centre on the site of the demolished Victoria swimming pool.
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In 2011, planning permission was granted for a 33-storey halls of residence, named the Blade, on the land but this has not been progressed.
Instead, the university drew up plans for a smaller building to expand its academic provision in humanities, law and business subjects.
A 'destination' restaurant and roof terrace are proposed for the upper floors.
A statement submitted with the application said the smaller building would 'significantly' reduce the amount of shade it creates.
'Whilst the more compact massing of the proposed building is wider than the thin edge of the Blade in the middle hours of the day, as the sun is at a much steeper angle during these hours, this was judged to be a good compromise to minimise the combined shadow area and overall impact on the park,' it said.
It added that 'only a very small area' in the southern part of the park would receive fewer than five hours of direct sunlight a day.
A sunlight assessment, commissioned by the university and submitted with its application, said there would be 'no significant impact' on the park.
However, with Portsmouth City Council in the process of bidding for funding for a multi-million pound overhaul of the park, including a new events space in this area, this claim has been questioned by Friends of Victoria Park in its formal objection to the application.
Its representative, Terry Pearson, said the proposed building would cause the park's ‘illusion of tranquillity’ to be ‘lost to future generations forever’.
‘This building may well be a good design, but this is the wrong place for it,’ he said. ‘Portsmouth does not want its people’s park to be a shadowland.’
‘Since Portsmouth is the most densely populated city in the UK outside London, it follows that we have the least amount of open space in the country per capita of population. We cannot afford to ruin what little we have.’
Similar concerns have been raised by the council's service manager for parks and also its landscape architect, Vincent Mount, who said the building would create 'considerable shade' over the south west of the park and ‘reduce its quality of tranquillity and refuge’.
But professor Graham Galbraith, the university's vice chancellor, said the building had been designed by 'world class architects' to minimise the impact on the park.
‘If we are granted planning approval, this will be a stunning landmark building designed for the future with flexible spaces for teaching, research and collaboration,’ he said.
‘We have set out to ensure that the design and landscaping complement the sensitive parkland setting and also that it has high standards of environmental sustainability.’
The application will be considered by council planning officers over the coming weeks.