She also is asked why she wore the 'I Really Don't Care Do You?' jacket to visit immigrant children who had been separated at the border by her husband's administration.
Trump said she supports women, but added that men need to be supported as well.
When asked if accused men have received unfair treatment, the first lady said there should be proof to support the accusations.
Trump responded that she does support the women behind the #MeToo movement - but noted that she supports men, too.
Saudi government planned Jamal Khashoggi hit: NY Times
Jamal Khashoggi was once considered an insider to the Saudi establishment with links to the security and intelligence apparatus. Khashoggi was last seen a week ago entering the consulate in Istanbul to get documents related to his forthcoming marriage.
Bulgaria detains suspect over killing of journalist
Bulgarian authorities filed charges against the man and were expecting Germany to transfer him to Bulgaria, the minister added. Bulgarian law enforcement is investigating all possible theories, but has warned people not to jump to groundless conclusions.
Osaka Pulls out of Hong Kong Open with Back Injury
The Argentine top seed Del Potro will face either Britain's fifth seed Kyle Edmund or unseeded Nikoloz Basilashvili of Georgia. Recently-crowned US Open champion Naomi Osaka has pulled out of the ongoing Hong Kong Open citing a back injury.
Without naming names, it's impossible to know if she's talking about any organizations that might have found it particularly uncomfortable to be associated with an administration that took hundreds of children from their parents and put them in cages last June to demonstrate its new zero-tolerance border policy, whose president has called protesting National Football League players "sons of bitches", and who insisted there were "good people on both sides" when white supremacists marched in Charlottesville - to name just a few situations that might have caused certain organizations and foundations to decide they needed to decline her offer to partner.
"I will move on that and I think that all the victims they need - we need to help all the victims no matter what kind of abuse they had, but I am against any kind of abuse or violence", she said.
The first lady, whose husband has faced allegations of inappropriate behaviour, also said women should have solid evidence to support their claims.
Trump was away on a trip to Kenya last week as Kavanaugh's confirmation hearing took place.
During the 2016 presidential campaign, at least 13 women accused Donald Trump of misbehavior ranging from sexual harassment to sexual assault.