Animal rights groups want it banned for good.
The draft law would also prohibit wild animals in circuses and the killing of pets.
Replacing the horse-drawn carriages with electric carriages would mean that "all parties will win out".
The carriage drivers say that the horses are in good condition.
Guillermo Amengual has been a constant critic of the current town hall administration.
According to a lawyer who specialises in animal rights, there was a lack of transparency regarding the cull which contravened European and Spanish laws.
"When an invasive species increases in an uncontrolled way, it attacks the ecosystem and jeopardises other species."
MEPs approved an amendment that EU money “should not be used for the financing of lethal bullfighting activities”.
“We are continuing to gain ground and achieve our aim of banning bullfighting in the Balearics."
“The atrocious death of this horse in its own stables is something which does not happen in the 21st century."
"The municipal vets are, in the meantime, carrying out three inspections a day, three days a week."