The step was taken a day after police registered an FIR following a complaint filed by Rai alleging that her email accounts were hacked and pictures were made public with an intention to outrage her modesty.
The Crime Branch of Delhi Police has registered a case in this regard under section 66A of IT Act and section 509 IPC (word, gesture or act intended to insult the modesty of a woman) following the complaint.
"We have forwarded her request to take down all objectionable photographs from social networking sites," a senior police official said.
A controversy had erupted after private pictures of Rai and Singh surfaced on social media following which the 67-year-old politician admitted to his relationship with her on Twitter on Wednesday.
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"I have no hesitation in accepting my relationship with Amrita Rai. She and her husband have already filed a mutual consent divorce case...Once that is decided we would formalize it," the former Chief Minister of Madhya Pradesh tweeted.
Singh's wife Asha passed away last year after prolonged illness. He has four daughters and a son from the marriage.
Rai, said to be in her early 40s, had also tweeted that she will marry Singh after divorce with her husband.
"I have separated from my husband and we have filed a mutual consent divorce papers. After which I have decided to marry with Digvijaya Singh," she tweeted.
Rai has alleged that her email account and computer were hacked.
"My email/computer (have) been hacked and contents tampered with. It is a serious crime in India and encroachment of my privacy. I strongly condemn it," she said in her tweet.