For animals, I would recommend Andy's suggestion and use "to pet".
1) Her dog likes to be petted.
2) May I pet you dog?
Perhaps it is merely a coincidence, but remember that an "animal de estimação" is a "pet" in English.
1) I have three pets: a dog that doesn't bark, a psychotic cat, and a goldfish that doesn't swim well.
2) No pets allowed.
"Pet" is also a term of endearment, something like "bemzinho", and it can be used much like "bomzinho".
I assume it is much more common in the UK than in the USA.
1) Hello, pet. You look lovely tonight.
2) Be a pet and bring me a drink.
3) Roger is so sweet. What a pet!
From an old rock and roll song:
"You're my baby
You're my pet
We fell in love on the night we met"
For humans, you will hear "to stroke" or "to caress".
1) He stroked her hair.
2) She caressed his hand.
Remember that for humans, "to pet" has a very different meaning. It is to fondle, to touch parts of the body normally covered by clothing.