BACKGROUND: Colonoscopy and the faecal immunochemical test are accepted strategies for colorectal cancer screening in the average-risk population (ie, people aged >/=50 years without personal or family history of colorectal cancer). In this trial, we aimed to compare whether invitation to screening with faecal immunochemical test was non-inferior to colonoscopy in a screening programme. METHODS: COLONPREV was a pragmatic, randomised, controlled, non-inferiority trial done at 15 tertiary hospitals across eight regions of Spain. Eligible participants were presumptively healthy and aged between 50 years and 69 years without a personal history of colorectal cancer, adenoma or inflammatory bowel disease, family history of hereditary or familial colorectal cancer (ie, two or more first-degree relatives with colorectal cancer or one diagnosed before age 60 years), severe comorbidities, or previous colectomy. Participants were randomly assigned (1:1) to one-time colonoscopy or biennial faecal immunochemical test before invitation to screening. The primary endpoint was colorectal cancer mortality at 10 years, assessed in the intention-to-screen population. An absolute difference of less than 0.16 percentage points was required to show non-inferiority. This trial was registered with ClinicalTrials.gov, NCT00906997. FINDINGS: Between June 1, 2009, and Dec 31, 2021, 57 404 individuals were randomly assigned to receive an invitation for colonoscopy (n=28 708) or the faecal immunochemical test (n=28 696). The intention-to-screen population consisted of 26 332 individuals in the colonoscopy group and 26 719 in the faecal immunochemical test group. In the intention-to-screen population, participation in any form of screening was 31.8% in the colonoscopy group and 39.9% in the faecal immunochemical test group (risk ratio [RR] 0.79 [95% CI 0.77 to 0.82]). Faecal immunochemical testing was non-inferior to colonoscopy with regard to the risk of colorectal cancer mortality at 10 years: the risk was 0.22% (55 deaths) in the colonoscopy group and 0.24% (60 deaths) in the faecal immunochemical test group (risk difference -0.02 [95% CI -0.10 to 0.06; RR 0.92 [95% CI 0.64 to 1.32]; p(non-inferiority)=0.0005). INTERPRETATION: Participation in screening was higher among individuals invited to faecal immunochemical test screening than colonoscopy screening. On the basis of participation observed in this study, a faecal immunochemical test-based programme was non-inferior to a colonoscopy-based programme for colorectal cancer-related mortality. FUNDING: Fundacion Cientifica de la Asociacion Espanola contra el Cancer and Instituto de Salud Carlos III.