Singh, who is likely to give a statement in Parliament on the issue, held a meeting with Delhi Lieutenant Governor Najeeb Jung and city Police Commissioner B S Bassi.
They briefed the Minister about yesterday's incident.
Singh said that the probe should be completed as soon as possible as it was a "sensitive" matter, officials said. [Farmer suicide: Suicide or abetment, 3 questions must be answered]
He also directed that necessary steps be taken to ensure that such an incident does not recur.
The farmer from Rajasthan committed suicide at the rally in full public view in the presence of Delhi Chief Minister Arvind Kejriwal at Jantar Mantar. [Farmer suicide: Gajendra Singh had tried his hand in politics]
The incident triggered a blame game among political rivals with demands being made that a case of murder be filed against AAP which had organised a rally against the Centre's land acquisition ordinance.
The Home Minister had yesterday directed Delhi Police to probe the incident.