Although the Ministry of Business, Innovation and Employment said it did not know how many companies were currently offering pet leave, Aidan Burch, its acting manager of employment standards, said it encouraged firms to think of unique ways to attract staff.
"We have a competitive labour market and we encourage companies to think outside the square in order to attract and retain top talent," Burch said.
"We encourage businesses thinking of offering 'paw-ternity' leave to consider the owners of fish, birds and other non-pawbearing pets. We wouldn't want them to be left out."
In 2015 the country's largest bank, ANZ, announced a flexible working scheme for all of its employees.
ANZ spokeswomen Emma Mellow said the bank recognised "mainstreaming flexibility had far-reaching impacts on the productivity, agility and connectivity of all staff."
"This includes the ability to work from a flexible location or with a flexible schedule, to support the balance between work and personal commitments. It's a broad policy that covers a lot of individual circumstances - not specifically a leave provision for new or sick pets," Mellow said.
Jacqui Baigeny, Animates national manager of brand and partnerships, said the pet shop did not have a "paw-ternity clause" for employees, but stroveto "support our people when it comes to human and fur kids".
"Whilst we don't have a paw-ternity clause, we do support our people to support their pets when needed. Should pets be in training or even recovery we support them to have them close by during those times in our many environments, but ensuring the safety and welfare of those pets in our environments comes first," Baigeny said.
Animates operated a roster for staff who wanted to bring pets to work, she said.
We encourage businesses thinking of offering 'paw-ternity' leave to consider the owners of fish, birds and other non-pawbearing pets. We wouldn't want them to be left out.
"In our support office environment we have a pet roster that is well articulated to include dog days, cat days, and a bird and exotic day. It's very important that with a pet roster the dynamic works well and all the pets are happy as we can have up to six dogs in the open plan office on a dog day which is a lot of fun for the pets and humans alike."
In Britain, almost one in 20 new pet owners have been offered "paw-ternity leave", according to research by pet insurance provider Petplan.
Manchester-based tech company BitSol Solutions offers employees a full week of paid leave if they get a new pet.
Company owner Greg Buchanan told Metro UK he understood the importance of time off when employees adopted a new pet. "Pets are like babies nowadays, so why shouldn't staff have some time off when they arrive?" he said.
United States firms Mars, Kimpton Hotels and Restaurants, Maxwell Health and VMware are reportedly offering three days of pet bereavement leave.
