Temporal patterns of oceanic predators can provide valuable information on both lunar and diel influences not just on the distributions of these predators, but also on prey patches that are often difficult to study. Mid-oceanic island chains in the northern Indian Ocean have high odontocete occurrence, but the ecology of these animals is not well characterized. We investigated fine-scale spatial and temporal patterns of island-associated odontocetes using passive acoustic monitoring from January 2019 to January 2020 around Kavaratti Island, Lakshadweep, India. Based on opportunistic recordings in the presence of odontocetes, the majority of the detected whistles were likely made by spinner dolphins Stenella longirostris. We identified a resident population whose whistle occurrence was significantly influenced by month, site, and diel and lunar cycles. More acoustic detections were made in the northeast monsoon month of November and fewer during pre-monsoon and southwest monsoon periods. Distinct day-night differences along with fine-scale temporal variability were also observed, suggesting that delphinids use nearshore waters as a daytime resting habitat. Odontocete detections were highest during the new moon period and lowest during the first quarter phase. Detection rates were higher on the south side of the island. Our study shows that solar and lunar cycles modulate odontocete vocal occurrence, presumably through influences on their prey. Similarities of odontocete occurrence around Lakshadweep to other mid-oceanic island chains suggests that an island-associated micronekton community may exist around Lakshadweep that may also be important to other pelagic species targeted by local fisheries.