Irani said she "appreciated" media for accosting his female collegues. "But I think it is for the gentleman to issue the statement and not me," she said.
Irani said she had repeated time and again on the issue, especially about women speaking out. "Anybody who is speaking out in no way should be shamed, victimised or mocked," she said.
"This is my only appeal to those witnessing this surge of outpouring of emotions of the anger on the internet and offline also," she added.
The Bharatiya Janata Party (BJP) leader's remarks came after the government faced flak from opposition parties over allegations of sexual harassment against Akbar by several female journalists and demanded his removal.
On Tuesday, Union Women and Child Development Minister Maneka Gandhi also supported the #MeToo movement which has caused a storm in the film industry and singed newsrooms, reaching the Modi government with Akbar being named.
Gandhi had said there should be an investigation.
"Those who are in positions of power always use it, whether it is film, media or industry. Whenever women make such allegations, we should take them very seriously," Gandhi had said.
At least seven women journalists have accused Akbar of sexual harassment and inappropriate behaviour when he was editor.
Akbar is currently on an official visit to Nigeria and has reportedly been asked to cut short his visit.