The 70-year-old ex-serviceman Ram Kishan Grewal from Haryana's Bhiwani district had allegedly consumed poison.
His native village in Haryana was flocked by political leaders including Rahul Gandhi and Arvind Kejriwal.
Earlier, Singh had said that the "mental state" of Grewal needed to be probed before drawing conclusions about his extreme action.
'If Modi is talking to every Tom, Dick and Harry, why is he afraid of talking to ex-servicemen?'
Here's a recap of events that occurred in India in the past 24 hours.
The Congress vice president asserted that OROP was the right of military personnel and the government "will have to give it".
The 70-year-old ex-serviceman Ram Kishan Grewal committed suicide by consuming poison at a park in New Delhi area on Tuesday evening.
Rahul was leading a candle light march organised by the Delhi Congress unit from Jantar Mantar to India Gate when police personnel restrained him
The delay in receiving the revised pension was due to problems in calculation at his bank's end.
"I urge the PM once again: soldiers should not have to struggle to claim what is their due. OROP must be implemented in a meaningful way! My heartfelt condolences to the family of Subedar Ram Kishan Grewal. Extremely sad to learn of his death," the Congress vice president said.