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Telomere length (TL) shortening has been identified as a marker of aging and associated with adverse health outcomes, but evidence of its association with sarcopenia is inconclusive. Estimate the cross-sectional and prospective associations between TL and sarcopenia. We used data from Waves 3 and 4 (2017, 2021) of the Study on Global Aging and Adult Health in Mexico (SAGE-Mexico). The cross-sectional sample consisted of 1,738 adults aged 50 and older, and the longitudinal sample consisted of 1,437. Relative TL was determined by real-time quantitative polymerase chain reaction (qPCR) on DNA extracted from saliva samples and quantified as the telomere/single-copy gene (T/S) ratio. Sarcopenia was defined according to the European Working Group on Sarcopenia in Older People (EWGSOP2). The mean salivary TL was 1.50 T/S units (95% CI: 1.49–1.52). The baseline prevalence of sarcopenia was 13.3% (95% CI: 9.8–16.8%). The incidence and persistence of sarcopenia were 6.8% (95% CI: 5.0–9.5%) and 7.0% (95% CI: 5.1–9.6%), respectively. The results showed that a one standard deviation decrease in TL was cross-sectionally associated with higher odds of sarcopenia (OR = 1.31; 95% CI: 1.03–1.67) and prospectively with a higher incidence (RRR = 1.55; 95% CI: 1.06–2.25) and persistence (RRR = 1.50; 95% CI: 1.01–2.24) of sarcopenia. Older adults with shorter TL had higher rates of incident and persistent sarcopenia. Implementation of interventions to delay the decline of TL in older adults is warranted. Further translational studies are needed to elucidate the effects of exercise or diet on DNA repair in the telomeric region and their associations with sarcopenia. [ABSTRACT FROM AUTHOR]