If elected, which appears to be a certainty, the 71- year-old former lawyer would be only the second Dalit to occupy the Rashtrapati Bhavan after K R Narayanan.
In a surprise move, the BJP announced that the low- profile Kovind was the National Democratic Alliance's presidential candidate for the July 17 poll.
"He was born in a poor family, comes from the Dalit community and has long struggled for the rights of the weaker sections. He has always been associated with the poor, backwards and Dalits... I am hopeful that there will be a consensus on his name," BJP president Amit Shah said at a press conference here.
The opposition will take a call on whether or not to put up a candidate against Kovind on June 22.
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Confident in the party's choice of a Dalit candidate, who had rarely ruffled any feathers during his years in politics, Prime Minister Narendra Modi tweeted, "I am sure Shri Ram Nath Kovind will make an exceptional President & continue to be a strong voice for the poor, downtrodden & marginalised."
The BJP's parliamentary board meeting, which was attended by Modi, picked the one-time Supreme Court lawyer after it went through a "long list" of names, Shah said, declining to reveal the other contenders.
Kovind, who flew to Delhi from Patna after the announcement, told NDTV, "It's a duty, let's take it as such."
The BJP's pick, a former two-time Rajya Sabha MP, known more as a Dalit champion than a Hindutva ideologue, had not figured in the names that were doing the rounds.
Modi also spoke to Congress chief Sonia Gandhi and former prime minister Manmohan Singh to seek their support for Kovind, whose election seems a virtual certainty given the NDA's numbers in parliament and assembly.
The Congress was unimpressed, however, and accused the ruling party of making a "unilateral announcement". The BJP's efforts for a consensus was nothing but a "PR exercise", said party leader Ghulam Nabi Azad.
"They informed us after announcing this decision so there is no scope for consensus now... We were not expecting this from the ruling party," he said.
As Trinamool Congress chief Mamata Banerjee expressed her reservations, her party colleague Derek O' Brien took a dig at the unassuming and relatively unknown Kovind. "How many of you logged onto Wikipedia today? I did," he said sarcastically.
An opposition leader said they might field former Congress minister and speaker Meira Kumar, also a Dalit, as their candidate.
However, there were also those in the opposition who kept their options open.
JD(U) chief and Bihar Chief Minister Nitish Kumar also expressed his "personal happiness" but did not commit his party's support.
Shiv Sena, a BJP ally which has played hot and cold over supporting it on the presidential candidate, said it would take a call soon.
But other parties like the TRS, which is in power in Telangana, were unambiguous in their support. YSRCP, an opposition party in Andhra Pradesh, has already offered its support.
The electoral college, which elects the president through the system of proportional representation, comprises elected MPs and members of state legislative assemblies -- a total of 4,896 voters including 4,120 MLAs and 776 elected MPs.
The total strength of the electoral college is 10,98,903.
The NDA is short of majority by barely 20,000 votes but with several non-NDA parties pledging their support to its candidate, the ruling block now enjoys a comfortable majority.
The BJP is also hopeful of support from the BJD and the AIADMK, which are in power in Odisha and Tamil Nadu respectively.