Singh alleged that the two parties were left with no issues and knew nothing about the 'one rank, one pension' matter.
"They have nothing else (no issue) to do politics on. That is why they do politics over dead bodies. Go and ask them whether they have attended funeral of any other soldier.
"So many soldiers have been martyred, did Aam Aadmi Party leaders and Congress leaders went to pay homage to them. They are talking senseless," the Minister of State for External Affairs told reporters on the sidelines of an energy efficiency conference.
Earlier on Wednesday, Singh had raised questions about the "mental state" of Ram Kishan Grewal, an army veteran whose suicide, allegedly over OROP, had sparked a political row.
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He had also rejected reports about Grewal being a prominent face of the 'One Rank-One Pension' agitation.
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Meanwhile, JD(U) leader K C Tyagi demanded resignation of General (retd.) Singh for his remarks on the suicide by ex-serviceman Grewal.
"I demand V K Singh's immediate resignation. I feel sorry that a person of such mindset became the army chief. He has insulted a jawan. There are still shortcomings in the OROP implementation even after 6th and 7th Pay Commissions' recommendations. The government should address them," he said.