Somatic cell nuclear transfer (NT) is associated with aberrant changes in epigenetic reprogramming that disrupt embryo development. Here, we characterized the epigenetic patterns of histone 3 lysine 9 trimethylation (H3K9me3) and histone 3 lysine 27 trimethylation (H3K27me3), the repressive histone signature in heterochromatin, in NT rabbit embryos. H3K9me3 modification was higher in all stages of NT vs. fertilized preimplantation embryos, consistent with decreased transcription of the H3K9me3 demethylase in four-cell and eight-cell NT embryos vs. fertilized embryos. H3K27me3 was higher in NT embryos from two-cell stage to the blastocyst, and transcription of the H3K27me3 demethylase was lower in four-cell and eight-cell NT embryos than in fertilized embryos. Cleavage under targets and tagmentation (CUT and Tag) showed enrichment of whole-chromosome H3K9me3 and H3K27me3 in four-cell and eight-cell NT vs. fertilized embryos. Further, eight-cell NT embryos had a higher proportion of H3K9me3 and H3K27me3 sites around the promoter regions of the genome compared to fertilized embryos. The genes associated with H3K9me3 sites near promoter regions were primarily related to the development of tissues and organs, whereas the H3K27me3 enriched regions mainly influenced the development and regulation of the nervous system. Our findings demonstrate that H3K9me3 and H3K27me3 inhibit the expression of genes essential for the development and preimplantation of NT embryos and, thus, are epigenetic barriers to NT reprogramming in rabbits.