The 10-member group set up by the opposition will meet for the first time after its constitution, sources said.
The opposition move on Wednesday's meeting came soon after BJP president Amit Shah announced that a panel of three senior ministers -- Rajnath Singh, Arun Jaitley and M Venkaiah Naidu -- would talk to allies and other parties on presidential candidates.
Several rounds of talks have already been held among senior opposition leaders on the issue. Congress president Sonia Gandhi has been trying to reach a consensus in the opposition on candidates for the presidential and vice presidential election.
A senior leader said if there was no consensus in the talks with the NDA, the opposition would put up a joint candidate against the NDA nominee.
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The sources said Congress leaders Ghulam Nabi Azad and Mallikarjun Kharge represent the Congress in the 10-member group, which also includes other senior opposition leaders such as JD-U's Sharad Yadav, RJD's Lalu Prasad and CPI-M's Sitaram Yechury.
DMK's Rajya Sabha member R S Bharathi, Samajwadi Party's Ram Gopal Yadav, Bahujan Samaj Party's Satish Chandra Misra, TMC's Derek O'Brien and NCP's Praful Patel are also on the panel.
Among the other names doing the rounds are those of former Speaker Meira Kumar and former Defence Minister Sharad Pawar, though the NCP strongman has said he is not in the race.
The poll to elect the next president will be held on July 17 and counting will take place on July 20.
The term of incumbent Pranab Mukherjee ends on July 24 and that of Vice President M Hamid Ansari on August 10.
After the meeting last month, Azad and Sharad Yadav read out a joint statement stating that in a presidential election, the ruling party traditionally took the initiative to build a consensus on candidates.
"This has not happened so far. If acceptable consensual candidates do not emerge, then we (opposition parties) shall field such persons who shall steadfastly defend the Constitutional values of our republic," the statement said.