Carbonates are key minerals for understanding ancient Martian environments because they are indicators of potentially habitable, neutral-to-alkaline water and may be an important reservoir for paleoatmospheric CO_2. Previous remote sensing studies have identified mostly Mg-rich carbonates, both in Martian dust and in a Late Noachian rock unit circumferential to the Isidis basin. Here we report evidence for older Fe- and/or Ca-rich carbonates exposed from the subsurface by impact craters and troughs. These carbonates are found in and around the Huygens basin northwest of Hellas, in western Noachis Terra between the Argyre basin and Valles Marineris, and in other isolated locations spread widely across the planet. In all cases they cooccur with or near phyllosilicates, and in Huygens basin specifically they occupy layered rocks exhumed from up to ~5 km depth. We discuss factors that might explain their observed regional distribution, arguments for why carbonates may be even more widespread in Noachian materials than presently appreciated and what could be gained by targeting these carbonates for further study with future orbital or landed missions to Mars