Sources said Singh admitted the mistake as the statement, which was read out in Rajya Sabha by the Home Minister, was cleared by him.
Under law and Supreme Court guidelines, names of rape and minor victims are not to be made public.
The Home Secretary apparently told Shinde that it was an oversight and since the statement was vetted by him, he takes full responsibility.
Home Ministry spokesperson K S Dhatwalia also refused to comment.
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Shinde had committed the gaffe on March 1 when he named the victims of the Bhandara rape incident in Rajya Sabha which had to be expunged at the intervention of the Leader of the Opposition Arun Jaitley.
Jaitley, a senior lawyer, had said as per law the victims of rape, that too minors, are not identified and named and their identity should be kept a secret as per Supreme Court guidelines.
Almost an hour after the Upper House had expunged the names of the rape victims, the Home Ministry circulated the text of Shinde's statement to media houses through a press release.