In a statement released through news agency ANI, the minister said he deemed it appropriate to step down and challenge the "false accusations" levelled against him also in a personal capacity.
Akbar's boss, Foreign Minister Sushma Swaraj, and Women and Child Welfare Minister Maneka Gandhi both were opposed to him continuing in office while he fought a legal battle against his accusers, the sources, who can not be named because of the sensitivity of the matter, said.
The resignation has come after much digging in of heels from Akbar who has hired a law firm, Karanjawala & Co., to file a defamation case against journalist Priya Ramani. His resignation comes in the wake of a series of allegations of sexual harassment levelled by at least 16 women. While Mr Akbar is entitled to all legal instruments available to a citizen to seek vindication, it would be paradoxical for a veteran editor to employ the instrument of criminal defamation.
The complaint has now been filed before a magisterial court at Patiala House through Karanjawala & Co. through its senior partner Sandeep Kapur along with Principal Associate Veer Sandhu, Senior Associates Niharika Karanjawala, Apoorva Pandey, Mayank Datta and Associate Gudipati G Kashyap.
Ms Ramani did not name anyone in the original piece, but said in her tweet that the article had been about Mr Akbar.
Akbar was accused of sexual harassment from his former colleagues during his stint as editor of The Asian Age. Akbar, she wrote, asked her to sit on his bed, "gesturing to a tiny space near you", which she declined to do. Now some of them are among India's most powerful women, heading the newsrooms of three English-language newspapers in the country and working internationally at major outlets like CNN and The New York Times.
She said that he would often insist on conducting interviews and meetings in hotel rooms.
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Women's groups and journalists' associations have demanded that Prime Minister Narendra Modi act against him.
The private complaint has sought prosecution of Ramani, who has accused Akbar of sexual misconduct around 20 years ago.
The BJP has tried to fashion itself as a champion of Indian women, arguing that policies to improve sanitation and switch to more efficient cooking fuels have disproportionately benefited them.
He termed these as "viral fever", saying these were "false and fabricated, spiced up by innuendo and malice", and added he would be "taking appropriate legal action". "Lies do not have legs, but they do contain poison, which can be whipped into a frenzy", he said.
Soon after Akbar resigned on Wednesday, the Congress stepped up its attack on Prime Minister Narendra Modi, demanding that he speak up on the issue.
Mr Akbar is a Rajya Sabha member belonging to the BJP.
But, clearly, there was a growing sense of unease and concern within.