The animal lover - who is the patron of seven animal charities - was called a "hypocrite" this week, after she said that animals didn't have rights because they didn't pay taxes, vote or have bank accounts.
But the royal, who is married to the Queen's cousin Prince Michael, said that she believes the furore was simply an issue of wording.
Princess Michael dismissed the debate was a 'misnomer'
Speaking exclusively to The Huffington Post UK at Kensington Palace, she said: "Well, it's expression of the words you use, isn't it?
"I'm involved very actively with three conservation charities, because I'm passionate about animals."
"But when you us the word rights, what do you mean? What do you actually mean when you say human rights? Animals don't have rights in that sense. The word is wrong.
"After all, if a predator, let's say a cheetah - kills a deer. What are the deer's rights? You know? You can't talk about rights in the same way. Does the cheetah have a right to kill the deer? What are the deer's rights if it's going to be killed?
She added: "We have enormous obligation to animals. I feel, personally, that humans have an obligation that we have to fulfill but when you say rights, you're talking about something quite different."
Princess Michael, 70, offended some people with her comments, which were made at the Henley Literary Festival when speaking about her new historical novel, Quicksilver.
Elisa Allen, associate director of PETA, told The Times it urged Princess Michael to study animal rights, "rather than making an off-the-cuff statement that reflects ignorance of the issue of what fundamental rights animals have, which do not include the right to drive a car or build up an overdraft."
"She should also exercise caution in opining at all on such issues, because her daft assessment would mean that children and certain classes of human beings are also not entitled to rights."
Princess Michael works with three conservation charities in Africa, and told HuffPost UK: "[My work is] Helping the animals in a practical way, making sure they have room and territory, this sort of thing. You can't start a law case on the part of the deer that's just been killed by the cheetah. It's just a misnomer."
"We need to protect animals, not go to court over them."
"So I think that obligation is the terminology, instead of the word 'rights', because humans have rights when they carry our certain activities: for their country, for their family, they perform their duties.
"Now, animals don't have duties as such. They look after their young, and very often the father isn't around and the mother brings up the cubs and the chicks or whatever. Do the chicks have no right to a father, or whatever? Rights is the wrong word in my opinion."
"It's a question of wording, we are there to help support the animals and I probably do more than lots of people. Charities who support animal rights are actually asking people to show their obligation by doing fundraising or similar."
She said she had been involved in creating 'corridors' for elephants in Africa, whose ancient travelling routes had been disrupted when villages were built in their path.
"The elephants trample through the villages, so then the villagers kill the elephants - you're going round in circles as to who has rights here. So what to do? well, I joined a group that moves the villages out of the way."
The royal is credited with convincing Battersea Dogs Home to add "cats" to its title after her husband was made a patron.
She is also the patron of the Arab Horse Society, the Furget-Me-Not Campaign for otters, The Bahamas Reef Enviroment Educational Foundation, The George Adamson Wildlife Preservation Trust, The Hoedspuit Endangered Species Centre, The Horse Rangers Association and The Ridgeway Trust for Endangered Cats as well as a supporter of other charities.
She was speaking to The Huffington Post UK as part of a forthcoming video interview on her upcoming book, Quicksilver, which is the third in the historical Anjou trilogy set in 15th century France.