Ms Trump made the comments during a remarkably rare TV interview, just days after Justice Kavanaugh’s contentious confirmation into one of the most highly esteemed legal roles in the US.
She told ABC: “I support the women, and they need to be heard.
“We need to support them – and also men – not just women.”
Primetime US TV show Good Morning America showed short clips from the extraordinary interview, which showed the First Lady reflecting on the #MeToo movement and her role in the White House.
During the interview, presenter Tom Llamas asked Melania if she believed men who had been accused of sexual assault had been “unfairly” treated, as members of the Republican Party and her husband have claimed.
Ms Trump responded: “You need to have really hard evidence.
“If you accuse someone of something, show the evidence.”
She added: “I do stand with women, but we need to show the evidence.
“You cannot just say to somebody, ‘I was sexually assaulted’ or ‘You did that to me.’
“Because, sometimes, the media goes too far.
“And the way they portray some stories – it’s not correct. It’s not right.”
The First Lady’s remarks come amid the recent furore surrounding Donald Trump’s nomination of Justice Brett Kavanaugh to the Supreme Court.
Justice Kavanaugh’s subsequent confirmation rocked the White House as angry protestors swamped Capitol Hill to voice their outrage.
During a campaign rally in Mississippi last week, President Trump urged his core base to “think of your son, think of your husband” in response to the scandal which he maintains is a conspiracy dreamt up by the Democrats.
Melania Trump also revealed some of the frustrations she felt about being First Lady during the unguarded ABC interview.
She called out groups that had refused to cooperate with her because of her husband’s politics.
She said: “It’s sad to see that organisations and foundations I want to partner with choose not to because of the administration.
“And I feel they are choosing the politics over helping others.”
But Melania refused to name the groups she was alluding to stating, “they know who they are.
“I don’t want to put them out in front of the world.”
The First Lady, who has been travelling the African continent on her first solo engagement, managed to avoid most of the drama and controversy surrounding Justice Kavanaugh’s confirmation to the Supreme Court.