"Opposition will meet on June 22, then only we can announce our decision", she added.
Kovind's nomination to the largely ceremonial post of president would be expected to garner enough votes from the BJP and its allies in an electoral college that brings together federal and state lawmakers.
Modi pointed out that Kovind, a farmer's son, comes from a humble background.
Prime Minister Narendra Modi tweeted that Kovind would "make an exceptional president" and "continue to be a strong voice for the poor, downtrodden and marginalised".
"Ram Nath Kovind has always fought for the betterment of the Dalits and other backward castes", BJP chief Amit Shah said at a press conference to announce the party's candidate.
Sources say a united Opposition could project either former Lok Sabha speaker Meira Kumar or former Home Minister Sushil Kumar Shinde - both Dalit leaders from Congress - as their joint nominee for the July 17 polls.
Union minister Nitin Gadkari said, "Under his leadership, India will prosper and the oppressed will get justice".
Born on 1 October 1945, at Derapur district, Uttar Pradesh, Ram Nath Kovind was elected twice to the Rajya Sabha in 1994-2000 and 2000-2006.
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.
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The van's 47-year-old driver, a white man who police believe acted alone, was detained by people at the scene. Several bunches of flowers had been deposited outside the mosque as commuters went to work on Monday morning.
The NCP on its part said it would take part in the Opposition meet on June 22.
As the vice president, he was the natural choice for the president's post in 1997 and all major parties, from the Congress to the BJP, supported him.
"Congress does not want to comment on this issue as we want to take a unanimous decision with all other opposition parties on the presidential elections".
Opposition parties have sought to keep up the suspense on extending their support and may even put up a joint candidate. He, however, said a detailed discussion would be held on the matter within the JD (U).
"We had full hope that before announcing they will discuss some names".
Stating that the prime minister spoke to him about the candidature of Ram Nath Kovind, Patnaik said, "He (PM) sought BJD's support in this regard".
The President has accepted the resignation of Ramnath Kovind as the Governor of Bihar a day after the National Democratic Alliance (NDA) named him as its Presidential nominee.
She, however, stopped short of expressing immediate support for Kovind saying the BSP will be positive provided the opposition does not field any Dalit for the top post.
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