Understanding the cognitive underpinnings of moral judgment is one of most pressing problems in psychological science. Classic studies suggest that intuition decreases utilitarian (expected welfare maximizing) judgments in sacrificial moral dilemmas, in which one has to decide whether to instrumentally harm (IH) one person to save a greater number of people. However, recent work suggests that such dilemmas are not fit for purpose as they fail to capture the defining core of utilitarianism, that is, commitment to impartial beneficence (IB). Accordingly, a new, two-dimensional model of utilitarian judgment has been proposed that distinguishes IH and IB. The role of intuition on this new model has not been studied. Does intuition disfavor utilitarian choices only along the dimension of instrumental harm or does it also do so along the dimension of impartial beneficence? To answer this question, we conducted three studies (total N = 970, two preregistered) using conceptual priming of intuition versus deliberation on moral judgments. Our evidence converges on an interaction effect, with intuition decreasing utilitarian judgments in IH - as suggested by previous work - but failing to do so in IB. These findings provide additional support to the recently proposed two-dimensional model of utilitarian moral judgment among ordinary people, and open up new avenues for future research.