This claim comes from a tweet. While some of the information is based on fact, there is more to the story. Overall, from what I have found, I would say that the list of 339 abducted children was provided to Russia by Ukraine. This list, though, was not a comprehensive list of all missing children from Ukraine. It was a small, unrepresentative list provided to encourage cooperation. Because Putin did not give a substantial response to this list, or in fact "no response" as one site listed below shares, Ukraine very naturally would have found this inadequate, especially considering the true gravity of the situation-- the fact that thousands of children were missing, not only 339. Thus, while there is some truth to this claim, the assertion that Ukraine was performing a PR stunt is likely not true and an exaggeration that was formed from out-of-context information. This "PR stunt" claim was not contextually accurate, as it did not consider the non-response by Russia to the minimal list presented compared to the thousands (likely 19,500 - 35,000 children, as stated by multiple sources below) predicted to be missing. If around 20,000 children are missing, as multiple sources contend, it would be quite fitting that Ukraine would claim Russia had failed to provide an adequate response to only 339 of them.
It is true that during their bilateral meeting held in Istanbul, Turkey, on June 2, 2025, Ukraine provided the Russian Federation with an "initial list of 339 Ukrainian children unlawfully deported to the Russian Federation or forcibly transferred from temporarily occupied areas of Ukraine." This information comes from https://www.diplomatie.gouv.fr/en/country-files/ukraine/news/article/statement-by-the-international-coalition-for-the-return-of-ukrainian-children#:~:text=During%20their%20bilateral%20meeting%20held,and%20it%20formally%20requested%20their which is a news source based in France that publishes information from all departments of the Ministry for Europe and Foreign Affairs. It is thus likely a reliable source. From this article, though, I think it is most important to take note of the use of the word "initial" when it refers to the given list.
Additionally, TIME, a global media source that has been in business for over 100 years and which produces popular articles such as TIME100 and TIME 100 Companies, corroborated the information that Russia received a list of 339 Ukrainian children. In this article, though, it is stated that the 339 children on the list were requested to be returned in addition to the estimated 1,200 Ukrainian children who were abducted and have since been returned home. In fact, "authorities in Kyiv say 19,546 children still need to be returned." In response to the given list of children, TIME states that Putin "gave no response." https://time.com/7302345/ukraine-lost-children-russia-war/?utm_source=beehiiv&utm_medium=email&utm_campaign=newsletter-the-brief&_bhlid=f623b10c56e9e40abbfcb349593acd49f0fad6e4
Again, this information is corroborated by Euronews (a European news source established in 1993), which states that "Ukraine has been able to verify Russia's deportation of 19,500 children to date... Only 1350 have been returned." https://www.euronews.com/2025/08/08/stolen-children-marketplace-russia-creates-catalogue-of-ukrainian-kids-for-adoption . This source, along with several others I looked at, also references Yale's Humanitarian Research Lab, which predicts the number of deported and missing Ukrainian children to be near 35,000. https://medicine.yale.edu/lab/khoshnood/give-now/ . Upon taking a brief look at Yale's Humanitarian Research Lab's (HRL) website, you can see the various research they have done on this issue. They have conducted multiple studies that have exposed and explored Russian programs and have identified thousands of Ukrainian children taken to Russia. In one NBC news article, the HRL is referred to as the "leading body tracking kidnapped Ukrainian children." With this coming from a well-known and reputable news source, this seems to suggest that the predictions coming from Yale may reasonably be the most accurate. NBC shares that to get much of its information, the group at Yale "has monitored the movement of children by analyzing satellite photos and photographing airplanes and vehicles apparently used to transport the kids," https://www.nbcnews.com/world/ukraine/fate-thousands-ukrainian-children-kidnapped-russia-hangs-balance-talks-rcna225074 .
Another source that had essentially the same findings as those listed above was https://www.theguardian.com/world/2025/jun/27/russia-ukrainian-children-abduction-war-crime . I also looked at "Bring Kids Back," a strategic action plan initiated by the President of Ukraine. The current numbers posted on their website indicate that there are 19,546 reports of Ukrainian children being unlawfully or forcibly deported or transferred, and that only 1,605 have been returned. https://www.bringkidsback.org.ua/