Coronavirus disease 2019 (COVID-19) outbreak that was declared as a pandemic by the World Health Organization (WHO) on 11 March 2020 has already had severe consequences in all aspects of people’s lives worldwide. The pandemic has affected over 200 countries and has become a major concern. India also faced a stiff challenge in terms of controlling the virus outbreak and through some strict measures such as nationwide lockdown was able to control the further spread of COVID-19 towards the latter part of 2020. Therefore, it is imperative to predict the spread of this virus along with causality analysis of parameters that play a significant role in its spread. The present study employs a series of univariate and multivariate time series forecasting techniques namely MSARIMA, ARMAX and extended VAR models to predict COVID-19 cases in New Delhi, Mumbai and Bengaluru. Besides, providing a robust forecasting performance for COVID-19 cases, the study also deals with finding the causal relationship of the spread of COVID-19 with various mobility and weather parameters. Outcomes of our study establish that the spread of COVID-19 can be associated with mobility and weather parameters apart from the various precautions that are taken by the people to reduce community transmission. However, the type of mobility (residential, retail and workplace) and type of weather conditions (air quality, temperature and humidity) associated with the causality differ with cities. For New Delhi, air quality, residential, retail are the parameters affecting the spread of the COVID-19 cases, whereas masks, temperature, residential and workplace were the significant mobility and weather parameters for Mumbai. In addition, for Bengaluru, the statistically significant causal variables were air quality, masks and residential. Outcomes of this study would help the concerned authorities to predict and contain future COVID-19 spreads in Indian cities efficiently.