Television footage of the protest close to the nation's parliament showed the farmer sitting in the branches of a tree before taking a scarf and hanging himself, as protesters, police and media crews looked on.
The farmer, reportedly a father of three from the desert state of Rajasthan, was rushed to hospital but declared dead on arrival.
"We are carrying out an inquiry about the entire sequence of events leading to Gajendra Singh's death... because when he climbed, several other people also climbed with him," joint police commissioner for Delhi, Mukesh Meena, told reporters.
Anger was mounting over whether police and rally organisers did enough to save the man, as a political row erupted over who was to blame for the suicide.
The tree was several metres from the stage where Delhi Chief Minister Arvind Kejriwal and members of his party were due to speak against the national government's land bill.
Local media said a suicide note had been recovered from the farmer's body, which said he had recently suffered crop losses because of unseasonal rains in Rajasthan.
Kejriwal and his Aam Aadmi (Common Man) Party (AAP) quickly came under fire from political opponents for continuing the rally even after the farmer was taken down from the tree.
"We want to ask AAP why they didn't stop their speeches when they heard that the farmer had died," Sambit Patra, spokesman for the Bharatiya Janata Party which rules at the national level, told reporters.
But Kejriwal put the blame on police, saying "he climbed the tree in front of our eyes."
"I kept telling the police to save him but the police are not in our control," Kejriwal said from the stage during the rally.
Scores of debt-laden farmers have suffered recent damage to their winter crops from unseasonal rains, with media reporting a string of suicides in recent weeks.
Protests have also been staged in the capital against Prime Minister Narendra Modi's push to overhaul the laws and make it easier to buy farmland for development projects.
The government argues the bill is needed to speed up economic growth, but political opponents say it favours big business at the expense of struggling farmers.
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