Councillor Sean Woodward said paramedics and lifeguards acted quickly to try and save the man but were unsuccessful.
The ambulance service said the man was in a ‘life-threatening condition’ when paramedics were called at 7.10pm yesterday.
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‘The man died in the swimming pool,’ Cllr Woodward told The News.
‘I am terribly sorry about this tragic incident, and my thoughts and prayers go out to the man’s family.
‘I would like to extend my gratitude to the lifeguards and paramedics for their hasty response, it was immediate.’
Multiple ambulance crews were at the centre in Park Lane.
Ryan Grant, contract manager at Everyone Active said: ‘A man became very unwell whilst using the pool.
‘Colleagues responded immediately, administering first aid until the emergency services arrived. Sadly the customer died at the scene.
‘Everyone Active would like to offer their sincere condolences to his family at this difficult time.’
A spokeswoman from South Central Ambulance Service said: ‘We were called yesterday to a patient in a life-threatening condition.
‘We sent a rapid response vehicle, two ambulance crews and the Hampshire and Isle of Wight Air Ambulance, who were all working at the scene to assess and treat the patient.
‘Sadly despite the attempts of our crews and people at the scene the patient passed away at the scene.’
Hampshire police were also on site by 7.10pm.
A spokeswoman said: ‘Police attended Fareham Leisure Centre at around 7.10pm on Sunday, November 14 following the sudden death of a man.
‘A file has been passed to the coroner.’
Fareham Leisure Centre reopened last month after a £6.2m refurbishment.
One witness who saw emergency services said there was a ‘relatively heavy ambulance/police presence’.
He added: ‘When I arrived around 6.15pm, someone was being stretchered into a waiting ambulance.
‘When I left at 8pm, there were probably three police cars and three paramedic vehicles in the car park.’