The former communications minister has moved to close a loophole in Irish laws that only bans the sending of abusive messages on the telephone network.
Pat Rabbitte has moved a bill in the Dáil on the same day his Labour party colleague, Senator Lorraine Higgins, published legislation calling for jail terms of up to 12 months for online trolling.
The bill would make it an offence to share any message that incites someone to commit harm to themselves.
If accepted the bill would provide for up to 12 months in jail, or fines of €5,000, for anyone guilty of cyberbullying.
Mr Rabbitte says he hopes that the legislation will become law - but he wants his legislation to be accepted to close a loophole in 2007 laws.
Senator Higgins has herself received death threats online, and says something needs to be done.