Climate change is potentially one of the most devastating problems, which leads to many disastrous extreme events. Understanding the relation between extreme climate indices (ECIs) and their potential drivers is required for statistical modeling, risk assessment and subsequent disaster preparedness. Most of the past studies considered the association of extreme precipitation indices (EPIs) with global climate oscillations, whereas the role of local meteorological variables (LMVs) on EPIs is often ignored. In this study, the association between three EPIs with four LMVs of three major Indian cities—Delhi, Mumbai, and Chennai over the 1981–2021 period are investigated using Wavelet transform coherence (WTC) approach. Bivariate and multivariate WTC analyses were employed to investigate the individual and combined influence of LMVs, such as relative humidity (RH), surface pressure (PS), surface wind speed at 2 m (WS2M), and temperature at 2 m (T2M), on EPIs. The study identified that significant coherence exists between the selected EPIs and LMVs, in which RH and PS have the most prominent influence on the indices. Local meteorological variables in a particular place highly influence the precipitation ECIs of that place and the dependency strength of dominant variables are influenced by the geographical characteristics and location. The joint role of LMVs and global climate oscillations together needs to be investigated as an extension problem for the subsequent modeling and risk assessments under climate extremes of these cities.