Bihar, West Bengal, and Uttar Pradesh were among the states which saw elections on Tuesday.
Voting was held in 38 of the 39 Lok Sabha seats in Tamil Nadu.
Counting for all the seven phases of voting will be taken up on 23 May.
Four states will also vote for the assembly in addition to the Lok Sabha.
The Election Commission of India is expected to announce the poll schedule soon.
India is both the largest and most diverse democracy, President Kovind pointed out.
VVPAT machines verify that votes polled in elections are reaching the correct candidate.