I would say the Kaiju genre, when it initially started out, was derivative of American Science Fiction/Monster Films of the time. Over time, the films began to have their own unique Japanese style, arguably starting with Mothra, with it's introduction of fantasy elements and a monster who was not the villain.
In a broader sense, they are fantasy/science fiction films because the films blend fantasy elements, like Mothra, with science fiction elements, such as the scientific justifications used for many of the monster's existence.
Still, particular films use certain stylistic criteria as they please. All Monsters Attack has elements of a children's film, A lot of the 70's films take have elements of Action films, Godzilla vs. The Sea Monster has elements of Adventure films ect.