Here are the latest developments:
A case will be registered for abetment, and death due to negligence, among other charges against as yet unnamed persons, the police said.
There were hundreds of people present at Delhi's Jantar Mantar when the man killed himself. There were layers of policemen deployed and a few metres from the tree where the farmer hanged himself, sat Delhi Chief Minister Arvind Kejriwal and other AAP leaders.
Before killing himself, Gajender Singh from Dausa district even flung what was perceived as a suicide note at the crowd, in which he had written: "I am a farmer's son. My father drove me out of the house because my crop failed. I have three children. I am from Rajasthan. Please tell me, how do I go home? Jai Jawan, Jai Kisan."
Four people climbed the tree to try to save the man after he was seen hanging. They released his body to a crowd below where people tried to catch it in plastic sheets. One of the men who climbed the tree to try and save the farmer alleged, "By the time I reached him, it was too late... I signalled to the policeman below for help. They did nothing, just stood around and laughed."
Mr Kejriwal has been criticised by the Congress and BJP for not stopping the event after the farmer died. The chief minister addressed the rally before visiting the hospital where the man's body was taken. He has accused the policemen deployed at the rally of doing nothing to save the farmer.
The Home ministry has asked the Delhi Police to investigate what happened. "Deeply pained to hear the news of a farmer committing suicide," Home Minister Rajnath Singh tweeted.
Prime Minister Narendra Modi also tweeted his condolences to the farmer's family, saying the death had "saddened the nation".
Gajender Singh will be cremated today around 10 am at his village in Dausa. Congress' Rajasthan unit chief Sachin Pilot is likely to attend the funeral.
The AAP rally was held at the city's Jantar Mantar, just a kilometre from Parliament, to protest against the Centre's proposed land reforms. Many prominent politicians including Arvind Kejriwal, Rahul Gandhi and Sitaram Yechury visited the hospital.
More than a dozen debt-ridden farmers have committed suicide in the country in recent weeks after crops were damaged by unseasonable rains and hailstorms. Farmers have also joined political rallies to express their anger at a proposed law to make it easier for businesses to buy farmland, that many fear will force them to sell land against their will.