COVID-19 is a highly infectious disease that is causing havoc to the entire world due to the newly discovered coronavirus SARS-CoV-2. In this study, the dynamics of COVID-19 for India and a few selected states with different demographic structures have been analyzed using a SEIRD epidemiological model. A systematic estimation of the basic reproductive ratio R0 is made for India and for each of the selected states. The study has analysed and predicted the dynamics of the temporal progression of the disease in Indian and the selected eight states: Andhra Pradesh, Chhattisgarh, Delhi, Gujarat, Madhya Pradesh, Maharashtra, Tamil Nadu, and Uttar Pradesh. For India, the most optimistic scenario with respect to duration of the epidemic shows, the peak of infection will appear before mid September with the estimated R0=1.917, from the SEIRD model. Further, we show, a Gaussian fit of the daily incidences also indicates the peak will appear around middle of August this year. Our analyses suggest, the earliest dates when the epidemic will start to decline in most states are between Jun-August. For India, the number of infected people at the time of peak will be around 1.6 million including asymptomatic people. If the community transmission is prohibited, then the epidemic will infect not more than 3.1 million people in India. We also compared India's position in containing the disease with two countries with higher and lower number of infections than India and show the early imposition of lockdown has reduced the number of infected cases significantly.