Singh, questioning the "conviction" of separatists, said they drew privileges such as air ticket concessions, sought subsidised treatment in hospitals or "lobbied" for their offspring in Delhi's "corridors of power".
"Despite this, they refused to abide by the Constitution of India," the minister said.
The MP from Udhampur in Jammu said separatism was never an "ideology" in Kashmir, but "more of a convenience than conviction".
"I bet, you again restore them to power and again they will start swearing by India and swearing Jammu Kashmir as a part of India. So this is the character of separatism and semi-separatism," the minister of state in the Prime Minister's Office said.
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His remarks were read as an attack on Abdullah, who was defeated in the 2014 Lok Sabha polls. His son, Omar, who was heading the National Conference government in the state, also lost power in 2014.
In the past, too, Singh had accused Abdullah of speaking the "language of separatists".
The minister was speaking at a seminar on the Indus water Treaty Conference organised by the Global Counter Terrorism Council.
He said had Jawaharlal Nehru as Prime Minister given "full control" to his Home Minister, Vallabhbhai Patel, to manage Kashmir, the situation would have been different today.
"Jammu and Kashmir became subject to a series of blunders and vested interests of the polity from time to time...History records what it describes as the infamous Nehruvian blunder over Kashmir," he said.
"After all, the buck has to stop somewhere," he added.
He said in his conversation with Kashmiri youth, he asked them to listen to separatists, but also question them if their sons were among the stone pelters.
"They (separatists) want their neighbour's child to become a stone pelter," he said.
"I could read out the names of these families who are lobbying in the corridors of powers in Delhi to get their children enrolled in different services though they don't subscribe to the Constitution of India," he said.
"This was the Kashmiri youth's conviction in the Indian Constitution," he said.