A register of animal abusers could help prevent offenders going on to commit violent crimes against people, Aberavon MP Stephen Kinnock has said.
He backed calls by the RSPCA for a log of those convicted and disqualified from keeping animals.
The charity said 11 people were prosecuted for breaching a ban in the last three years - and they believe the figure could be higher.
The UK government said it feared a public register could help vigilantism.
But the RSPCA said it would allow pet shops and rehoming centres to carry out a simple background checks on prospective buyers.
Mr Kinnock said he backed the RSPCA's calls following a case in his constituency where a teenager was sent to a young offenders institute after he stole cats from an animal sanctuary to use as "live bait" for his dogs.
It came two weeks after the 18-year-old was sentenced in a youth court for killing a sheep.
Mr Kinnock said: "I think it would be useful to have a register, perhaps something at least that pet shops would have access to, so someone like this would be prevented from having a pet and from buying an animal to keep as a pet in the future."
He said he had written to the Department of Environment, Food and Rural Affairs (Defra) to ask why there was not already a register.
"They told me that they don't have a register because they're worried about data protection issues," he said.
"Well, quite frankly, I don't think that's good enough."
He added: "I believe people who abuse animals are, I think, more likely to potentially go on to commit crimes - violent crimes - against a person, against people.
"And so, therefore, it would be very good from a crime prevention point of view to keep a register so that we can have zero tolerance of abusing animals and also as a way of then tracking people who could potentially go on to commit violent crimes against other human beings."
Jenna Satterley told BBC Radio Wales' Good Morning Wales she approached politicians with the idea of a register after being shocked by news stories of animals being abused in Wales.
Her petition calling for action has received support from more than 224,000 people.
"Somebody needs to stand up and say something publically and work on getting new laws implemented or old laws updated," she said.
Defra said people convicted of animal cruelty or abuse were already logged on the Police National Computer but added the UK government felt there needed to be better sharing of information on existing databases.
"The government agrees with the police that a publicly available register of animal abusers could facilitate vigilantism," a spokesman said.
"Instead, if a person has concerns about another individual they can approach the police who can check their records on the Police National Computer. The police may then take the most appropriate action.
"We consider that this is the best arrangement."