The remarks came as a growing number of South Korean women accused prominent figures of sex abuse, making headlines in the country that remains deeply conservative despite economic and technological advances.
"I express my respect to the courage of the victims who spoke out about the abuses they suffered, and I actively support the #MeToo movement," Moon said in a meeting with aides.
"The law enforcement authorities should respond to these courageous acts of victims by actively launching investigations," he said, urging "stern punishment" for offenders regardless of their backgrounds.
The #MeToo movement which kicked off a campaign against sexual misconduct by powerful figures in Hollywood and other industries, initially met with a relatively muted response in the deeply patriarchal South.
Fears of relentless public shaming and online bullying have made women reluctant to share their stories.
But an elite South Korean prosecutor made a rare move of appearing on live television last month to speak out about the sexual harassment she suffered at the hands of another senior lawyer in 2010.
Seo Ji-Hyeon said her career suffered a serious setback after she reported the case to her bosses.
Seo's remarks triggered a flood of testimonies as other women came forward to share their own experiences of sexual abuse at the hands of prominent men, including famous actors, a filmmaker, renowned theatre directors and a Catholic priest.
The South's Catholic church on Sunday apologised to a woman who accused a priest of sexually harassing her and repeatedly trying to rape her during a trip to a mission in South Sudan in 2011.
Moon, who has repeatedly voiced his support for women's rights, filled 30 percent of his cabinet seats with women -- a record -- and his government last year announced harsher punishments for sexual harassment in the public sector.
But on Monday the president said the problem "can't be tackled with the laws alone".
"It can be solved only by changing the culture and our way of mind," he said.
"We need to use this momentum to expose the problem no matter how humiliating and shameful it is."