A de novo G608G mutation in LMNA gene leads to Hutchinson-Gilford progeria syndrome. Mice lacking the prelamin A-processing metalloprotease, Zmpste24, recapitulate many of the progeroid features of Hutchinson-Gilford progeria syndrome. Here we show that A-type lamins interact with SUV39H1, and prelamin A/progerin exhibits enhanced binding capacity to SUV39H1, protecting it from proteasomal degradation and, consequently, increasing H3K9me3 levels. Depletion of Suv39h1 reduces H3K9me3 levels, restores DNA repair capacity and delays senescence in progeroid cells. Remarkably, loss of Suv39h1 in Zmpste24(-/-) mice delays body weight loss, increases bone mineral density and extends lifespan by ∼60%. Thus, increased H3K9me3 levels, possibly mediated by enhanced Suv39h1 stability in the presence of prelamin A/progerin, compromise genome maintenance, which in turn contributes to accelerated senescence in laminopathy-based premature aging. Our study provides an explanation for epigenetic alterations in Hutchinson-Gilford progeria syndrome and a potential strategy for intervention by targeting SUV39H1-mediated heterochromatin remodelling.