Aaron Carter is denying allegations he’s abusing his dog, Nala … and says he won’t give the pug to a rescue org offering big bucks for the pup.

Here’s the deal … folks are accusing Aaron of abusing Nala by allegedly keeping her in a crate outdoors in 100-degree heat and locked in bathrooms for multiple hours a day. People are also alarmed over Aaron’s new German Shepherds, worrying the big dogs could harm little Nala.

Some people even called Lancaster Animal Control on Aaron … and Nala’s got a trending hashtag, #SaveNala, which caught the attention of a pug rescue organization, The Pug Queen.

The org’s founder, Izabella St. James, tells us she reached out to Aaron offering him $10,000 to rescue the pug and rehome Nala, but claims the singer threatened her with a lawsuit for defamation.

Aaron tells 360aproko … the abuse allegations are absolutely not true. He says he only had Nala in a crate for 15 minutes to separate her from his new guard dogs.

AC acknowledges animal control came to his house, but claims officers concluded he did nothing wrong and … and left after he explained he was simply separating his new pets.

Bottom line … Aaron’s determined Nala isn’t leaving his care.