Machine learning has proven to be a powerful tool for the identification of distinctive genomic signatures among viral sequences. Such signatures are motifs present in the viral genome that differentiate species or variants. In the context of SARS-CoV-2, the identification of such signatures can contribute to taxonomic and phylogenetic studies, help in recognizing and defining distinct emerging variants, and focus the characterization of functional properties of polymorphic gene products. Here, we study KEVOLVE, an approach based on a genetic algorithm with a machine learning kernel, to identify several genomic signatures based on minimal sets of k-mers. In a comparative study, in which we analyzed large SARS-CoV-2 genome dataset, KEVOLVE performed better in identifying variant-discriminative signatures than several gold-standard reference statistical tools. Subsequently, these signatures were characterized to highlight potential biological functions. The majority were associated with known mutations among the different variants, with respect to functional and pathological impact based on available literature. Notably, we found show evidence of new motifs, specifically in the Omicron variant, some of which include silent mutations, indicating potentially novel, variant-specific virulence determinants. The source code of the method and additional resources are available at: https://github.com/bioinfoUQAM/KEVOLVE.