The Indian president is the ceremonial head of state, who plays decisive roles only in case of a hung parliament after general elections.
Senior Biju Janata Dal (BJD) leader and Agriculture Minister Damodar Rout said he voted for Kovind as the regional party has extended its support to the NDA candidate.
On Monday, members of the BJP's Parliamentary Board, the party's key decision-making body, will meet to discuss its choice for the vice-presidential poll.
Sources, however, maintained that the second meeting was cancelled as the MLAs did not want president of the Odisha Pradesh Congress Committee (OPCC) Prasad Harichandan to attend it.
"We have the support of 21 chief ministers and more than 30 political parties", said Kovind's campaign manager Bhupendra Yadav.
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Former Lok Sabha speaker Meira is backed by the Congress and 17 opposition parties, including the Samajwadi Party, Bahujan Samaj Party, NCP, AAP and the Trinamool Congress. Voting Starts: The voting for the 14th President of the country started today and the counting will take place on July 20th in New Delhi.
The term of President Pranab Mukherjee is expiring on July 25.
At an all-party meeting here, Modi said that a consensus candidate would have been better. It may be mentioned that the total number of vote's share of the MLAs and MPs in Meghalaya is 31,444. The EC also gave permission to five MLAs to vote in the Parliament in New Delhi.
"Kovindji will win with a comfortable and respectable margin", Information and Broadcasting Minister Venkaiah Naidu said before voting.
While the presidential poll is being seen as a contest between two Dalit leaders, Kumar had, at a conference earlier this month, described it as a "battle of ideologies".