At a luncheon meeting called by Congress president Sonia Gandhi on Friday, 17 opposition parties made a decision to form a committee to consider possible candidates to take on the government nominees in the elections.
Mr Kumar who was invited for a luncheon meeting of opposition leaders, called by Ms Gandhi, skipped the event and instead sent former JD (U) chief Sharad Yadav to represent his party on the occasion.
Asked about the reason for the JD-U President not attending the meet, Tyagi said, "He is busy with some important work of the government and won't be able to come".
The main opposition Congress is seeking greater unity among non-NDA parties ahead of the presidential election which could be taken forward to the upcoming assembly polls in states such as Gujarat, Himachal Pradesh and Karnataka, besides the Lok Sabha elections in 2019.
Senior Congress leaders, including party vice-president Rahul Gandhi, Mallikarjuna Kharge, Ahmed Patel and Ghulam Nabi Azad attended the meet as well. Mamata said no names were discussed at the lunch-cum-meeting at the Parliament House Library.
However, his absence on Friday at the luncheon meeting convened by Gandhi to discuss the issue set off speculation that something could be amiss in the opposition camp, more so after the recent Income Tax raids on the properties of RJD chief Lalu Prasad's kin.
She said a small committee would be formed by the opposition leaders, who met over lunch, in case they have to choose a nominee. Opposition leaders struck a cautious note publicly, but privately maintained that this show of strength will not be limited to the presidential election and will be given concrete shape over the next two years.
The BJP has a clear edge in the presidential election due to support of some parties outside the ruling National Democratic Alliance.
On joining PM's lunch tomorrow, Kumar said he accepted the invitation as the Chief Minister of Bihar.
Talking to reporters, Mayawati said the condition of Dalits, people belonging to weaker sections, religious minorities, poor and farmers has deteriorated in the three years of NDA government.
They also expressed concern over the prevailing grave situation in Jammu and Kashmir.
CPI's Sudhakar Reddy said the opposition parties may wait for the ruling alliance to announce a candidate "till the announcement of presidential polls".
Apart from West Bengal Chief Minister Mamata Banerjee and CPI-M's Sitaram Yechury, BSP's Mayawati and SP's Akhilesh Yadav, sat under one platform and attended the lunch together with other opposition leaders - NCPs' Sharad Pawar, RJD supremo Lalu Prasad and DMK's Kanimozhi.