Prime Minister Narendra Modi's ruling Bharatiya Janata Party is backing 71-year-old Ram Nath Kovind, a lawyer-turned-politician considered the favorite to take over the largely ceremonial post.
Kovind is also backed by several regional parties.
His main rival is Meira Kumar, 72, who was India's first female speaker of the parliament and a former federal minister. She is backed by main opposition Indian National Congress party.
The contest has been described in Indian media as "Dalit versus Dalit", a reference to the low caste origins of the two contenders.
The victor will replace Pranab Mukherjee, a former senior member of the Congress party, as the next occupant of Rashtrapati Bhawan, the massive 340-room, colonial era presidential palace. The BJP commands the most votes in parliament and in the states.
Results from the vote are expected on July 20.
"The presidential poll this time is historic".
"Every political party has kept in mind the dignity of this election".
Sonia Gandhi, the head of the Congress party, appealed to members of parliament to vote for Kumar to protect India's secular values.
The BJP has over two-thirds majority in the Lok Sabha, or lower house of parliament, and runs governments by itself or in alliance with other parties in 17 of India's 29 states.
The victor of the contest will be India's second president belonging to the Dalit community, after KR Narayanan, who was president between 1997-2002.
Dalits, formerly known as untouchables, are on the lowest rank of India's tradition social system based on caste.
Some presidents, such as outgoing President Pranab Mukherjee, have tried to act as conscience-keepers, using their constitutional authority as the head of state to defend India's founding principles as a secular, diverse democracy.