The number of dog thefts has increased by more than 50% in just 12 months, according to new figures.
In 2019 the PSNI recorded 27 dog thefts across its 11 policing districts.
Last year, despite strict lockdown measures, this increased to 41 thefts (up 52%). Since 2018 there have been a total of 107 dog thefts here.
The Belfast city policing district recorded the most in the last three years at 27, followed by Newry, Mourne and Down at 15. The district with the fewest reported thefts (two) was Ards and North Down, followed by Causeway Coast and Glens with three.
The Dogs Trust said the figures reflected a UK-wide trend, with traffic to the theft page on its website increasing by 780% since the start of the year.
Chief executive Owen Sharp added: "Demand for dogs is at an all-time high. Our research has shown that prices for some of the UK's most desirable breeds are at their highest in three years, and possibly ever, with the costs for some dogs increasing month-on-month since lockdown began.
"Given the high demand for dogs and the increase in prices, it is no wonder criminals are taking advantage of the situation."
With thousands of the pets being stolen, Mr Sharp urged the authorities to get tougher.
"Current sentencing does very little to deter thieves and does not take into consideration how devastating it can be to have a dog taken from you," he said.
"Punishment for dog theft is determined by the monetary value of the dog, meaning perpetrators are often given fines which do not reflect the emotional impact of dog theft on the families involved.
"We fully support any action to introduce tougher sentences that will act as a deterrent for those committing these crimes. At the least, a community order or custodial sentence should be given, rather than a fine."
Belfast councillor Anthony Flynn, who seconded a recently successful motion aimed at tackling the third-party sale of puppies, urged pet owners to take steps to keep their animals safe.
"There are a number of things we can do to try and deal with this incredibly worrying problem," he said.
"Dogs should not be seen as a commodity. People need to be much more aware of where their pets are and ensure they're in a safe place. Don't just keep them on a lead chained up outside.
"Dogs need to be trained so that, if they go missing and run off, they can find their way back. They must have good recall. Dogs also need to be microchipped.
"These are practical steps, but people also need to keep an eye out in their own area.
"If they see strange vehicles driving around, make a note of it and report it to community police teams. It's vitally important that police have up-to-date information to help them tackle this issue."
The Department of Agriculture, Environment and Rural Affairs is currently considering options for a ban on the third-party sale of puppies and kittens.
It follows a petition submitted to the Assembly calling for the extension of 'Lucy's law' to Northern Ireland. Such legislation would require anyone seeking to purchase a puppy or kitten to deal directly with a breeder, rather than buying from a third-party seller.