Background: ANRS IPERGAY found that on-demand pre-exposure prophylaxis (PrEP) with oral tenofovir disoproxil fumarate plus emtricitabine was associated with an 86% relative reduction of HIV-1 incidence compared with placebo among men who have sex with men at high risk of HIV. We aimed to investigate whether on-demand PrEP was similarly effective among individuals with lower exposure to HIV risk. Methods: Participants in the ANRS IPERGAY trial were randomly assigned to receive PrEP (fixed-dose combination of 300 mg tenofovir disoproxil fumarate and 200 mg emtricitabine per pill) or placebo. The primary endpoint was the diagnosis of HIV-1 infection. Pill uptake was assessed by counting returned pills at each follow-up and by estimating tenofovir concentration from frozen plasma samples. Participants were interviewed at each visit to assess the pattern of PrEP use. All participants enrolled in the modified intention-to-treat population of the double-blind phase of the ANRS IPERGAY trial were eligible for this post-hoc analysis. We calculated the total follow-up time for periods of less frequent sexual intercourse with high PrEP adherence (15 pills or fewer per month taken systematically or often during sexual intercourse). To estimate the time of HIV acquisition, fourth-generation HIV-1/2 ELISA assays, plasma HIV-1 RNA assays, and western blot analyses were done with use of frozen samples, and the stage of HIV infection was defined according to Fiebig staging. HIV incidence was compared between the two treatment groups among individuals who had less frequent sexual intercourse with high PrEP adherence. The ANRS IPERGAY trial is registered with ClinicalTrials.gov, NCT01473472. Findings: 400 participants who were randomly assigned to receive PrEP (n=199) or placebo (n=201) between Feb 22, 2012, and Oct 17, 2014, were included in this analysis. 270 participants had at least one period of less frequent sexual intercourse with high PrEP adherence during the study, representing 134 person-years of follow-up and 31% of the total study follow-up. During these periods, participants in both groups reported a median of 5·0 (IQR 2·0-10·0) episodes of sexual intercourse per month and used a median of 9·5 (6·0-13·0) pills per month. Six HIV-1 infections were diagnosed in the placebo group (HIV incidence of 9·2 per 100 person-years; 95% CI 3·4-20·1) and none were diagnosed in the tenofovir disoproxil fumarate plus emtricitabine arm (HIV incidence of 0 per 100 person-years; 0-5·4; p=0·013), with a relative reduction of HIV incidence of 100% (95% CI 39-100). Interpretation: A choice between daily or on-demand PrEP regimens could be offered to men who have sex with men who have less frequent sexual intercourse.