A cafe patron is trying to woo Amu – she of the long hair and lovely green eyes – but the beauty disdainfully turns away.

And then she flicks her fluffy tail. Amu is a long-haired calico – one of 51 felines who staff the Calico Cat Cafe, one of Japan's numerous cat cafes – and she has a reputation for being somewhat aloof.

But most of the resident felines are curious about the cafe customers and eager to toss a few toy mice around with them. Patrons, who pay 1000 yen ($A10) for an hour of cat play, can also get a cup of tea or a bite to eat. For another 300 yen, they can make a cat's day and buy a fortunate feline a small chicken snack.

The cat cafe didn't originate in Japan, but in the past decade it has really taken hold in a country where space is at a premium and many apartments and houses are too small to keep a pet.

The concept spread from Japan to Europe, where cafes such as the Katzencafe in Berlin and La Gatoteca in Madrid have opened. Now it has leapt to the US, with the grand opening of the Cat Town Cafe in California in October. Australia's first cat cafe opened in Melbourne last June.

The Japanese fixation on cats goes back to a time when the cats that gobbled up rats and silkworms were considered the lucky charms of the silk industry.

Now Japanese affection for the feline is evident in cartoon characters like Krocchi, a swashbuckling stray cat, the catlike girl character Hello Kitty, and the ubiquitous Maneki-neko, the beckoning cat figurine whose raised paw is thought to bring good luck and good fortune.

There's even a cat shrine on Tashirojima Island, where the cats greet the returning fishing boats. During the 2011 earthquake and tsunami, it's said that the cats who wander the island evacuated to the area around the Neko-jinja, or cat shrine, and survived. Another island, Aoshima, where the cats outnumber the people, also has become something of a tourist attraction for cat lovers.

Takafumi Fukui, owner of the Calico in Toyko's Shinjuku neighbourhood and another cafe in Kichijoji, said the cat cafe was born in Taiwan, but was far different from what it's become in Japan. There, he said, the cats wandered in and out from the street, mingling with patrons as they sipped tea.

At the Calico, an elevator whooshes patrons up to the sixth-floor reception area where they are expected to park their shoes and don slippers, put jackets, purses or luggage into a locker, and scrub their hands and apply a hand sanitiser before heading in to see the cats.

The reception area smells vaguely of eau de cat litter, but the floor below where the main cat room and the cafe are is odourless. The litter boxes are set up in an area under the stairs. "It's a lot of work; we clean them frequently," Fukui said.

The Calico Cafe – the largest cat cafe in Tokyo – is a cat paradise, with scratching posts, kitty tree houses, perches, cardboard boxes and baskets to hide in, sunny window sills to lounge on, and feathery toys and cloth mice to swipe at.

Kurumi Bonkohara, a first-time visitor, swished some feathers at one of the cats and tried a pair of velvet bat wings on another. "I've been to cat cafes all over Japan, but this one is by far the biggest one I've visited and the cats are really friendly here," she said.

An album at the cafe includes each cat's breed, birthdate and personality traits. It says Amu is "arrogant in the store but timid outside".

The cats are allowed to wander freely between the fifth and sixth floors, but there are rules for the people. Only beverages are permitted on the cat-play floor; more substantial food can be bought in a separate glass-enclosed room where cats aren't allowed. About half the patrons supplement their cat fix with food.

Flash photography is prohibited, and most importantly, there is this rule: "Please do not wake up the sleeping cats, surprise them or annoy the cats."

About 40 cats work the floor at the same time. Cats who don't get along work different shifts, and each cat has its own cage in a private room. They spend the night in their cages and are fed in them to ensure that each cat gets the correct diet.

"When we opened our first cafe about eight years ago, the concept of the cat cafe wasn't really established, so we had to explain it," Fukui said. "Now the business is doing well, and we are starting to get a lot more foreigners."

Fukui said his family kept five to 10 cats when he was a child. "My first reason for wanting to open a cat cafe was so I would be able to keep a lot of cats," he said.

Now he has 20 varieties – Persians, ruddy Ocicats, Norwegians, Siamese, Ragamuffins, Abyssinians, Scottish Folds, a short-legged Munchkin born on Christmas Day named Santa, American Shorthairs and more. The biggest is Taiga, a Maine Coon cat.

"In Tokyo it's hard to keep pets because the apartments are so small, and I thought many people might feel the same way I did," he said. New arrivals to the city who used to keep cats, and now can't, also find their way to the cafe for cat therapy.