The Scottish SPCA is now appealing for information after rescuing the cats at a residence at Harvester's Way in Edinburgh at about 6pm on Sunday.
The animals are being cared for at the charity's Edinburgh and Lothians Animal Rescue and Rehoming Centre at Balerno.
The five-month-old cats – two females and two males – have been named Fifi, Trixie, Ryan and Finn.
Animal rescue officer Melissa Maitland said: "The people who found them said they were in a box at the bottom of the stairwell.
"It's incredibly sad to see yet more animals being dumped at this time of year. Hopefully we will be able to find all four loving, permanent homes, where they will receive the care and attention they deserve."
On the same day, also in Edinburgh, a dying hamster was found abandoned in a toilet cubicle at an Asda store. Ms Maitland took the animal to the same rescue centre in Balerno, where it was discovered it had a fatal tumour and it died overnight.
She said: "Whoever dumped him clearly had no intention of getting him the veterinary attention he needed. It is not only cruel to abandon an animal, it's also a criminal offence, and we're keen to find the person responsible."