The application of U isotopes in carbonates as a paleo-ocean oxygenation proxy is based on the critical assumption that the calcareous shell-building organisms incorporate U into their shells without fractionation relative to the U isotopic composition of ambient seawater. Recent studies claim a small, but resolvable, isotopic offset during abiotic and biogenic aragonite precipitation, whereas no isotope fractionation has been recorded during calcite precipitation. Although aragonite is meta-stable and not preserved over geological timescales (>1 Myr) and U precipitates during diagenesis, the U isotope composition of biogenic aragonite is important because aragonite precipitation is an important U sink to carbonate sediments. In contrast, low-magnesium calcite (LMC) is preserved over geological timescales and may provide a reliable fingerprint of ancient ocean chemistry. Therefore, a more general study is needed that compares U isotope compositions of primary marine biogenic carbonate precipitates. We report the U isotope compositions of 32 modern samples from geographically distinct localities in the Atlantic Ocean including corals (Scleractinia, Octocorallia), brachiopods (Articulata), molluscs (Tellina Listeri, Codahia Obicularis) and barnacles as well as one fossil mollusc. These samples reflect variable primary minerals, water temperatures, water depths, pH-values of ambient water, and U concentrations. Several seawater samples have also been measured to compare our methods with those of previously published studies. The analyzed modern corals and brachiopods display U isotopic compositions that are indistinguishable from modern seawater. This suggests that these carbonates have the potential to faithfully record the U isotopic composition of the surrounding seawater in which they form. The analyzed brachiopods are of particular interest as they are composed of the calcium carbonate polymorph LMC that is stable over geological timescales. While this study shows for the first time that LMC phases are robust targets in ancient samples, their low U abundance presents analytical challenges for precise U isotope analyses. We also show that two barnacle shells collected with ambient seawater have U isotopic compositions that are both lighter and heavier than the ambient seawater. The mechanism to explain this offset is not determined, but it demonstrates that at least barnacle shells are not representative of the seawater in which they last lived. Two of three partially fossilized mollusc shells also show resolvable offsets from seawater, likely indicating secondary processes that are known to shift or fractionate U isotopes. Collectively, our new data indicate that: 1) aragonite delivers U with a seawater composition to carbonate sediments, and 2) LMC shells of brachiopods that are stable over geological timescales may be more suitable for reconstructing the U isotope composition of ancient oceans.