Aim To test if training and support, financial reimbursement and option of referring screen‐positive patients to an internet‐based method of giving advice (eBI) can increase primary health‐care providers' delivery of Alcohol Use Disorders Identification Test (AUDIT)‐C‐based screening and advice to heavy drinkers. Design Cluster randomized factorial trial with 12‐week implementation and measurement period. Setting Primary health‐care units (PHCU) in different locations throughout Catalonia, England, the Netherlands, Poland and Sweden. Participants A total of 120 PHCU, 24 in each of Catalonia, England, the Netherlands, Poland and Sweden. Interventions PHCUs were randomized to one of eight groups: care as usual, training and support (TS), financial reimbursement (FR) and eBI; paired combinations of TS, FR and eBI, and all of FR, TS and eBI. Measurements The primary outcome measure was the proportion of eligible adult (age 18+ years) patients screened during a 12‐week implementation period. Secondary outcome measures were proportion of screen‐positive patients advised; and proportion of consulting adult patients given an intervention (screening and advice to screen‐positives) during the same 12‐week implementation period. Findings During a 4‐week baseline measurement period, the proportion of consulting adult patients who were screened for their alcohol consumption was 0.059 per PHCU (95% CI 0.034 to 0.084). Based on the factorial design, the ratio of the logged proportion screened during the 12‐week implementation period was 1.48 (95% CI = 1.13–1.95) in PHCU that received TS versus PHCU that did not receive TS; for FR, the ratio was 2.00 (95% CI = 1.56–2.56). The option of referral to eBI did not lead to a higher proportion of patients screened. The ratio for TS plus FR was 2.34 (95% CI = 1.77–3.10), and the ratio for TS plus FR plus eBI was1.68 (95% CI = 1.11–2.53). Conclusions Providing primary health‐care units with training, support and financial reimbursement for delivering Alcohol Use Disorders Identification Test‐C‐based screening and advice to heavy drinkers increases screening for alcohol consumption. Providing primary health‐care units with the option of referring screen‐positive patients to an internet‐based method of giving advice does not appear to increase screening for alcohol consumption.