Kovind, the former Bihar governor, is contesting against the opposition's joint candidate and former Lok Sabha speaker Meira Kumar.
"Kovind ji will win (the election) with a respectable and comfortable margin," Union minister M Venkaiah Naidu told reporters ahead of the polling.
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The CPI(M), which is backing Meira Kumar, urged voters, comprising MPs and MLAs, to pick the "custodian of the Constitution" thoughtfully.
"Hope the Electoral College picks the custodian of India's Constitution thoughtfully: Vote to uphold Constitutional Values of our Republic," party general secretary Sitaram Yechury said on Twitter.
With both Kovind and Kumar belonging to the Dalit community, Bahujan Samaj Party (BSP) chief Mayawati expressed satisfaction that a Dalit leader would occupy office of the president irrespective of who won the poll.
Mayawati also claimed it was because of her party that the NDA and the opposition had to field candidates from the community.
"Winning or losing (a poll) is a different issue. Whoever wins, the good thing is a Scheduled Caste person will be the country's president. And I think it is a good thing for our movement, the party.
"And the NDA, the BJP had to field a Dalit candidate for the presidential poll because of the BSP and the other side (the opposition) too," she told reporters outside Parliament.
The voting for the presidential poll began at 10 AM today and will continue till 5 PM.
The results of the poll will be declared on July 20.
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