A main breeding target of the International Potato Center (CIP) has been the biofortification of potato (Solanum tuberosum L.) with the essential micronutrients iron and zinc. This study assessed the broad‐sense heritability (H 2) and genetic gains (ΔGs) achieved for iron and zinc concentrations in potato tubers and their relationships with yield components through three cycles of recurrent selection at the diploid level. Sixty genotypes comprising 17 Andean landraces from a base population called Cycle 0, 21 genotypes from Cycle II, and 22 from Cycle III were grown in field trials over 2 yr to compare micronutrient concentrations and agronomic performance. The effects of cycles and cycles × location interactions were both significant (P < .01) for all characters except tuber yield. High phenotypic and genotypic coefficients of variation along with high H 2 (0.81 ± 0.19 for both iron and zinc) suggested that these parameters were under the control of additive gene effects and could be effectively manipulated by recurrent selection. Large gains of more than 29% iron and 26% zinc were demonstrated. There were slight decreases in dry matter (DM) content of 2 and 5% in Cycles II and III, respectively. Iron concentration had the greatest positive direct effect on total number of tubers per plant, and zinc had a weak negative direct effect on average tuber weight. Selected iron‐ and zinc‐dense genotypes with high, positive general combining ability were identified for use in an interploidy (4x –2x ) breeding scheme aimed at increasing the iron and zinc contents of stable, high‐yielding disease and stress‐resistant varieties.