Yes, domestic cats can and sometimes do kill rabbits. A rabbit falls under the classification of lagomorph (hares, rabbits and pikas). Predation by domestic cats on lagomorphs is more commonplace on the young of the species. The secondary question, therefore, is whether domestic cats kill rabbits of the same size as the cat. The answer to that is yes as well but as stated it is less common. This is because their size is near the upper limit for prey animals of the domestic cat. However, the vast majority of cat studies show that small mammals, principally rodents and rabbits or hares are the dominant prey.
I hope that answers the question about rabbits adequately because there is nothing really more to say.
Sources: BM Fitzgerald – The diet of domestic cats and their impact on prey populations in The domestic cat: The biology of its behavior AND P Leyhausen – Cat behavior: The predatory and social behavior of domestic and wild cats.
FYI – some people say that domestic cats are not good rat killers. The truth is that adult Norway rats are sometimes killed by cats but studies show that few domestic or community cats will attack an aggressive adult Norway rat. However, where Norway rat numbers have been reduced by the efforts of local residents or the local authority cat predation has been shown to be effective in keeping the rat population to low levels. At high levels of rat population domestic cats are ineffective.
Sources: As above (second reference) and CS Elton – The use of cats in farm rat control 1953.
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