The Taoiseach has told the Dáil there can be no tolerance of bullying or sexual harassment in the workplace.
He was responding to Labour TD Joan Burton, who asked if the matter had been discussed by Cabinet.
"There can be no tolerance in my view of assault or sexual harassment or bullying of any sort in any workplace. I want that message to go out very clearly," Mr Varadkar said.
Yesterday Minister of State Mary Mitchell O'Connor raised concerns about sexist behaviour she claims to have witnessed in the Dáil.
In relation to the Gate Theatre, he said while they are a private institution, it was incumbent on them to put in place an independent investigation.
A number of women have been speaking out about alleged incidents involving Michael Colgan, the former artistic director at the Gate.
He said he had discussed the matter with Minister for Culture Heather Humphreys, who is due to meet the Arts Council to see if action needed to be taken across the arts sector.
However, he added that he did not believe for a second that issues such as bullying or sexual harassment are unique to any one sector and are probably prevalent in society.
He also said he was "full of admiration" for those who had come forward to speak out here and abroad.
He said this would make people who may consider treating fellow workers in such a beastly manner to think twice.