The first two published PubMed articles I found when researching the topic make contrasting claims. The first, written in 2010 by Naturopathic Medicine doctor Walter J. Crinnion, claims that studies indicate higher amounts of iron, magnesium, and vitamin C can be found in organic food. He does not, however, provide any linked sources to back up his claim.
The second article was written in 2024 by a team of students studying at the Center for Climate Change Research at the University of Toronto. It states that “All in all, the evidence was not strong enough to suggest that organic foods are more nutritious than non-organic foods.” There were four sources cited showing differences in the nutritional values of certain organic crops, but a lot of reported differences could be attributed to both farming practices and study biases.
The Mayo Clinic and an article published by UC Davis back up the claims in the second PubMed article, stating that “Organic doesn't automatically mean the food has more nutrients,” and “Organic foods are not healthier, per se, in terms of nutrients. You are still getting the same benefits in conventionally grown foods as you are in organic foods.” So, the consensus seems to range from “unsure” to “probably not”.
The idea that organic foods are more nutrient-dense than non-organic foods likely originates from a false assumption, as the consumption of organic foods is proven to have many other health benefits due to the lack of pesticides and harmful chemicals used. It’s also possible that there's lobbying from organic food producers to overstate the benefits of consuming organic food, given that biased studies are being produced. That being said, it can be concluded from the information above that this claim is false.
Sources:
PubMed Article 1: https://pubmed.ncbi.nlm.nih.gov/20359265/
PubMed Article 2: https://pmc.ncbi.nlm.nih.gov/articles/PMC10814746/
https://www.mayoclinic.org/healthy-lifestyle/nutrition-and-healthy-eating/in-depth/organic-food/art-20043880
https://health.ucdavis.edu/blog/good-food/are-organic-foods-really-healthier-two-pediatricians-break-it-down/2019/04