MOTIVATION: Genomic data sharing beacon protocol, developed by the Global Alliance for Genomics and Health (GA4GH), offers a privacy-preserving mechanism for querying genomic datasets while restricting direct data access. Despite their design, beacons remain vulnerable to privacy attacks. This study introduces a novel privacy vulnerability of the protocol: One can reconstruct large portions of the genomes of all beacon participants by only using the summary statistics reported by the protocol. RESULTS: We introduce a novel optimization-based algorithm that leverages beacon responses and single nucleotide polymorphism (SNP) correlations for reconstruction. By optimizing for the SNP correlations and allele frequencies, the proposed approach achieves genome reconstruction with a substantially higher F1-score (70%) compared to baseline methods (45%) on beacons generated using individuals from the HapMap and OpenSNP datasets. We show that reconstructed genomes can be used by downstream applications such as in membership inference attacks against other beacons. Our findings reveal that beacons releasing allele frequencies substantially increases the reconstruction risk, underscoring the need for enhanced privacy-preserving mechanisms to protect genomic data. AVAILABILITY AND IMPLEMENTATION: Our implementation is available at https://github.com/ASAP-Bilkent/Beacon-Reconstruction-Attack. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.