Here are the top 10 updates on this big story:
The meeting, which was clouded by the absence of five key parties, saw some disagreement over a three-page statement criticising Prime Minister Narendra Modi and the government, which came up at the last minute. The parties finally agreed to take four lines for their statement to the media.
West Bengal Chief Minister Mamata Banerjee, who called the meeting, told reporters later that the opposition needed to sit together to discuss "the bulldozing taking place in the country".
Ms Banerjee had invited 22 parties but 16 attended the meeting. They decided on a June 21 deadline for naming a presidential candidate versus the nominee of the BJP and its allies. "Mamata Banerjee, Sharad Pawar and Congress leader Mallikarjun Kharge will consult with various parties to build consensus on a name," said DMK leader TR Baalu.
After Sharad Pawar, 81, turned down Mamata Banerjee's offer to be the opposition's presidential candidate, no one had any other suggestion. At the end of the meeting, she took the names of Gopal Gandhi and National Conference leader Farooq Abdullah.
Sharad Pawar had the support of many parties, including Mamata Banerjee's Trinamool Congress, Left, the Congress and the Shiv Sena. "If Sharad Pawar agreed, everybody will give him support. But Pawar-ji does not agree, we will discuss," Ms Banerjee told reporters.
In a tweet, Mr Pawar said, "I sincerely appreciate the leaders of opposition parties for suggesting my name as a candidate for the election of the President of India, at the meeting held in Delhi. However, I like to state that I have humbly declined the proposal of my candidature."
The presidential elections will take place on July 18 and the results will be declared on July 21. June 29 is the last date for nominations.
While Mamata Banerjee's rivals Congress and Left attended the meeting, leaders like Telangana Chief Minister K Chandrashekar Rao - who had bonded with his Bengal counterpart over their common goal of defeating the BJP - decided to boycott it. The TRS said there was "no question of sharing any platform with the Congress".
The Akali Dal and the Aam Aadmi Party (AAP) also opted out, protesting the Congress' presence. AAP said it will "consider the matter only after the Presidential candidate is declared".
Jagan Mohan Reddy's YSR Congress and Asaduddin Owaisi's AIMIM were not invited. We have not been invited and we would not have attended because Congress party has been invited," Mr Owaisi said.
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