The request, which has been tabled on the city council’s website, said the situation for residents had reached “breaking point”.
The e-petition relates to the SO14 postcode, which covers areas like the city centre, Northam and Bevois.
It says: “Residents are exhausted, frustrated, and fed up with the council’s inaction on this long-standing issue.
“Every day, we face impossible challenges finding parking, endure sleepless nights trying to secure spaces, and are unfairly penalized with exorbitant fines.
“This is no longer an inconvenience – it’s a crisis that affects our mental well-being, family life, and finances.
“We have had enough of the council ignoring our needs while allowing this problem to escalate.”
The petition is “demanding” the council to take “immediate and decisive” action.
Suggested measures put forward include increasing parking capacity by allocating additional spaces exclusively for residents and opening underused car parks during peak hours.
It also recommends introducing a grace period before issuing parking tickets and a suspension of fines in areas where parking is insufficient.
Both these ideas are listed under a heading of “stop predatory fines”.
The last suggestion is to develop and share a long-term parking strategy with resident input and reinvest parking revenue into local infrastructure.
The petition adds: “This crisis impacts mental health, finances, and quality of life. Residents deserve better. We demand immediate action from Southampton City Council to solve this problem now.”
If a petition receives more than 1,500 signatures, it is debated at a full council meeting, with the organiser of the petition given the opportunity to present it before it is discussed by councillors.
There are currently five signatures on the parking e-petition, which runs until January 23.
More details can be found at southampton.gov.uk/moderngov/mgEPetitionDisplay.aspx?ID=500000163&RPID=635949966&HPID=635949966