- Left says presidential election is a must, it is 'battle of ideologies'
- Left suggests Meira Kumar, Sushil Kumar Shinde of Congress
- Opposition parties to meet on Thursday in Delhi on next move
Here are the 10 latest developments in this big story:
Congress leader Ghulam Nabi Azad was in Patna on Tuesday for an Iftar celebration - the meal that breaks the roza or fast during Ramzan - hosted by the Congress. His visit is allowing him key consultations with heavyweights Lalu Yadav and Bihar Chief Minister Nitish Kumar.
The opposition had earlier said it would wait to see the government's pick for President before deciding whether to support its nominee or force an election on July 17.
The selection of Mr Kovind, 71, has made it difficult for leaders to reject him. He is a Dalit, and few parties would risk alienating the politically vital community by being seen as obstacles to Mr Kovind's promotion. If elected, he will be India's second Dalit president after K R Narayanan, who served from 1997 to 2002.
Mayawati, for example, has already said that she supports the selection of a Dalit for Rashtrapati Bhawan, the presidential palace in Delhi.
Similarly, the Bihar Chief Minister has been effusive in his praise of Mr Kovind, who, he said, maintained immaculate neutrality while Governor despite his BJP standing.
Mr Kovind's nomination allows the BJP, traditionally perceived as a party with upper-caste Hindus as its supporters, to build upon its considerable outreach to lower caste voters and to unglue the opposition as one large combined front.
Mr Kumar's Janata Dal United or JDU will meet in Patna today to decide whether, despite its high esteem of Mr Kovind, it will support a candidate against him in a show of solidarity with other opposition parties. Mr Kumar's ally, Lalu Yadav, is, according to sources in favour of an election.
Congress chief Sonia Gandhi is expected to chair Thursday's meeting of the opposition. The Left says her party should present former Home Minister Sushil Kumar Shinde or former Lok Sabha Speaker Meira Kumar as presidential options to other parties.
While the Congress is keen on an election, it is reportedly concerned that putting up a candidate will telegraph its failure in uniting the opposition if constituents like Mr Kumar and Mayawati choose not to be on the team.
The BJP and its allies, with the backing of regional parties - including the Shiv Sena which pledged support on Tuesday - should be able to get Mr Kovind elected smoothly. Those in the opposition who want their own candidate believe it will signal their fighting spirit to the public as well as allow them to test how effective a combined front might be against Prime Minister Narendra Modi in the general election in 2019.