Hours before a Sunday newspaper hit the stands with revelations about Patrick Nulty, he said he was immediately standing down as an Independent TD (Teachta Dala, member of the Dail) for Dublin West.
"I sent inappropriate messages via Facebook," he said, in a statement.
"This included inadvertently sending one to a 17-year-old woman. To the best of my knowledge I have never met this woman and the message was sent while under the influence of alcohol."
The former Labour Party TD, who left the junior coalition government partner last June in a row about the political direction it was taking, apologised "wholeheartedly" to the girl involved and to her family.
"It was never my intention to upset anyone in this way but it was totally wrong," he said.
The Sunday World newspaper claims Mr Nulty, 31, asked a schoolgirl in a late night Facebook message: "Have you ever been spanked?"
It is further alleged that a woman was asked to send underwear in the post and another was urged to wear a skirt when visiting a constituency clinic.
The newspaper said it confronted the TD with "geo-tagging" evidence claiming the messages were sent from inside Leinster House, which is home to the Irish Republic's houses of parliament.
Mr Nulty was elected to the Dail in 2011 under a Labour Party ticket, taking the late former Finance Minister Brian Lenihan's seat.
In his statement he said the message was entirely inappropriate and that he took full responsibility for his actions.
"I set myself the highest standards personally and politically," he said.
"Unfortunately due to personal mistakes I have not met those standards in this matter and I will take responsibility for that."
Mr Nulty thanked his family, friends and supporters.
"In politics people very often do not take responsibility for their actions," he said.
"I hope I am doing that. I would further like to apologise to my constituents in Dublin West for my mistake.
"I hope they will understand my reasons for resigning and accept my apology.
"I hope that as I have taken decisive and direct action on this matter my privacy will now be respected in what has been a very difficult decision for me personally."