The petition, which has gathered just under 3,200 signatures in three days follows a court case last week in which a horse owner avoided jail despite one of her animals dying while left unattended for two weeks.
Clare Hopkins, of Tukes Avenue in Gosport, admitted three offences over the horses in Newgate Lane, Fareham, and was handed an eight-week prison sentence, suspended for 12 months, a £300 fine and was banned from keeping horses for three years.
Four horses have been left in her family’s care.
A woman from Wickham, who did not wish to be named but knows the horses well, said: ‘This is an issue that is at the heart of our community and needs to be dealt with.
‘The other horses cannot be left to suffer in the same conditions. Something needs to be done quickly.’
There are four horses still on the land and the petition calls for their removal stating that given the ‘historical evidence of neglect’ on the land, the animals should be removed under the Animal Welfare Act 2006.
The act states: ‘It’s an offence to cause unnecessary suffering to any animal.’
Rebecca Johnson, who set up the petition said: ‘The punishment given to Clare Hopkins was woefully inadequate in our opinion and the horses remaining are in real danger over time of becoming the next victims.’
The petition will be submitted to both Fareham Borough Council and the RSPCA.
Councillor Sean Woodward, leader of the council said: ‘I am a horse lover myself and I support any means necessary to prevent animal cruelty.’
Hopkins was also given 20 days of rehabilitation activities and ordered to repay vet costs of £274.80.
A spokeswoman for the RSPCA said: ‘The RSPCA has been made aware of concerns for the welfare of horses kept at Newgate Lane and has been along to check on them with a specialist vet on Tuesday.
‘We want to reassure people that they are receiving food and water and are in good health.’
She added: ‘The field the horses are being kept in is not ideal but we have given advice to the owners about improving this environment.’