Calls to make pet theft a specific criminal offence have been rejected by ministers, who say it is covered by existing laws.
Campaigners argue stiffer penalties are needed to deter thieves.
And a petition urging government to act has gathered more than 250,000 names.
But the Labour MP who chairs the Commons Petitions Committee said pet theft was “spiralling” upwards and described the government’s response as “incredibly disappointing”.
In a letter to Justice Secretary Robert Buckland, Catherine McKinnell said: “Pet theft is a truly callous crime. It strikes at the heart of families and the evidence is showing that every year the government fails to take action the problem is getting worse.
She said ensuring sentencing options were available to courts would act “as a real deterrent for those who commit pet theft crimes”.
‘Through the roof’
In reply, Mr Buckland said: “The government fully understands the deep distress caused by the theft of a much-loved family pet and the importance of dealing with pet theft given this impact it can have on owners.
“However, I should reiterate that stealing a pet is already a criminal offence under the Theft Act 1968 for which the maximum penalty is seven years’ imprisonment.”
He said the government was “satisfied” that the existing law was sufficient and had no plans to introduce a new specific offence to deal with the theft of pets.
Giving evidence to the Petitions Committee in June, editor of Dogs Today magazine, Beverley Cuddy, said instances of pet theft during the coronavirus lockdown had “gone through the roof”.
“Unfortunately in lockdown everyone wanted a dog and the prices went up and up and the criminals looked at those figures and looked at all those people who wanted dogs and put two and two together,” she said.
She said a tougher deterrent was needed, arguing: “They have taken a member of the family hostage and by not having anything in place which makes this a serious crime we are enabling the most emotionally draining thing to happen to people.”