Control operations for invasive ship rats, Rattus rattus, in New Zealand forests are often followed by increased house mouse, Mus musculus, detections suggesting rats suppress mice. A potential mechanism is intraguild predation, either by interference competition or as simple predatory behaviour. If aggression by rats towards mice is mainly competitive, it should include threat and display features associated with, for example, intraspecific fighting. If predatory, it should lack these features and be associated with feeding. In the first of two captive experiments we observed interactions between paired, live rodents, either side of a wire-mesh screen, and found that most rats were aggressive to mice. This aggression lacked threat and display characteristics typical of encounters with conspecifics and was rarely reciprocated by mice. In a second experiment, euthanized mice were drawn by a line through cages occupied by rats fed either a restricted or unrestricted diet. Rats of both groups attacked and restrained the euthanized mice, and all rats that interacted with the mice ate at least part of them, although food-restricted rats tended to eat more. As the aggressive response of ship rats towards mice lacked threat and display features and was related to feeding, we conclude that it resembles predatory behaviour. Our findings provide a better understanding of the interactions between ship rats and house mice, which hinder their management where they coexist as damaging invaders. However, further research is required to determine whether the results of our captive experiments are consistent with wild rat behaviour.