Modi made a veiled attack on Jawaharlal Nehru as he said the country's "fate" and "face" would have been different if Patel had been the first Prime Minister.
Singh immediately hit back by questioning Modi's claim over Patel's legacy, saying the late leader was secular and liberal to the core, having respect for those with different ideology.
Modi, who spoke first at the function to inaugurate a museum in memory of Patel, said, "every Indian regrets that he (Patel) did not become the first Prime Minister. Had he been the first Prime Minister, the country's fate would have been different, its face would have been different."
Modi credited the first Home Minister with uniting the country after Independence and said the same unity and integrity was under threat from terrorism and maoism at present.
Responding to Modi's barbs, Singh appeared to question the Gujarat Chief Minister's claim on Patel's legacy as he underlined that he was a Congressman and secular.
"Sardar Patel was secular to the core. He had a deep faith in the integrity of India. He believed that the whole country was a village and people of all communities here were his relatives and friends," Singh said.