It is a long-standing debate as to whether or not the annual modulation in the event rate observed by the DAMA sodium iodide experiment is caused by the interaction of dark matter particles. To resolve this issue, several groups have been working to develop new experiments with the aim of reproducing or refuting DAMA's results using the same sodium iodide target medium. The COSINE-100 experiment is one of these that is currently operating with 106 kg of low-background sodium iodide crystals at the Yangyang underground laboratory. Analysis of the initial 59.5 days of COSINE-100 data showed that the annual modulation signal reported by DAMA is inconsistent with explanation using spin-independent interaction of weakly interacting massive particles (WIMPs), a favored candidate of dark matter particles, with sodium or iodine nuclei in the context of the standard halo mode. However, this first result left open interpretations using certain alternative dark matter models, dark matter halo distributions, and detector responses that could allow room for consistency between DAMA and COSINE-100. Here we present new results from over 1.7 years of COSINE-100 operation with improved event selection and energy threshold reduced from 2 keV to 1 keV. We find an order of magnitude improvement in sensitivity, sufficient for the first time to strongly constrain these alternative scenarios, as well as to further strengthen the previously observed inconsistency with the WIMP-nucleon spin-independent interaction hypothesis.