More women should come out and address the issue of sexual harassment and narrate their experiences, Gandhi said.
"I believe in all of them. I believe in the pain and trauma behind every single complainant," she told PTI in an interview.
Gandhi did not comment on the allegations of sexual harassment against her colleague M J Akbar, who has been accused by several former women colleagues of sexual harassment when he served as editor at various media organisations.
The minister of state for external affairs, film director Sajid Khan and actor Alok Nath are among those accused of sexual misconduct and more.
"I am proposing to set up a committee with senior judicial and legal persons as members to look into all issues emanating from the #MeToo campaign," Gandhi told PTI in an interview.
The committee will look into the legal and institutional framework in place for handling complaints of sexual harassment, including some of the complaints if required, and advise the ministry on how to strengthen these, the WCD minister said.
"It takes a lot for women to come out like this. These cases have been elephants in the rooms for the last 25 years. The question here is how can they prove these after all these years... they have faced verbal assault, they have been touched, pinched, their clothes have been pulled...
"The first thing to do is naming and shaming these monsters. Naming and shaming will go a long way in lessening the pain these women have been carrying," she said.
The next step, she said, is to set up a committee that can listen to the women.
Urging women to come out with their stories, Gandhi said men who sexually harass them depend on them to be shamed into keeping quiet.
She said her ministry has created a woman friendly environment in which they can complain to her directly. Even anonymous complaints will be addressed.
Gandhi said women could complain through the She Box (www.shebox.nic.in), which provides a single window access to every woman, irrespective of her work status to register complaints related to sexual harassment.
Complaints can also be lodged at min-wcd@nic.in, she said. All the cases will be closely monitored by the ministry.
"Regarding taking action against those that are in office, I am really hopeful that the system will react because I believe that these complaints are true," she said.
According to the minister, protecting women has been the watchword of the present government with the Beti Bachao Beti Padhao campaign one of its flagship schemes.
"The prime minister has always given top priority to the rights of women. The first programme that he launched was Beti Bachao Beti Padhao. We don't save our daughters to allow big shots to insult them later in life.
"I will do what I can do to help them," she said, adding that women should raise their voices.
"They should speak out and in one jolt finish off this matter altogether so that men are frightened from ever sexually assaulting or making women uncomfortable."
India's #MeToo movement, which started with Tanushree Dutta alleging that actor Nana Patekar harassed her during a film shoot in 2008, has escalated sharply with increasing numbers of women coming forward with their complaints.
Demands for action against Akbar have also been rising.
While most BJP leaders and ministers have refrained from commenting, on Thursday, Textiles Minister Smriti Irani said Akbar himself would be better positioned to speak on the issue.
She urged people not to mock women speaking out against the harassment meted out to them.
"That is my only appeal to everybody who is witnessing this surge of outpouring of emotion, of anger on the internet and offline also," she said in Mumbai.
'Predators need to be named and shamed'
How you can avoid #MeToo at work
Will Modi ask Akbar to step down?
BJP likely to seek Akbar's explanation before taking action
#MeToo movement sweeps into Indian media