Lawyers for Michael Sean Quinn, 24, claimed comments posted on anti-abuse campaigner Joe McCloskey's personal page threaten the safety of him and his family.
Quinn, originally from Glasvey Drive, Twinbrook, is seeking an injunction against Mr McCloskey and the social networking giant to have the contents removed from the site.
He was jailed for eight years in 2007 for raping a teenage girl. Quinn attacked his victim, 15, in the city in August 2005 while she was on holiday from England.
During the trial, it emerged that he later used the girl's mobile phone to call her mother and state: "I enjoyed raping your girl."
Following his release from jail, he was returned to custody for breaching a sexual offences prevention order.
In court on Friday, Quinn's counsel, Michael Ward, confirmed he was seeking an order for the removal of Mr McCloskey's personal page.
The barrister said "inflammatory" comments posted on it by other users referred to what should be done to his client.
"These comments constitute a threat to the personal safety of, not only him, but also his family," Mr Ward claimed.
He told Mr Justice Horner how, last month, police notified Quinn that he was under threat.
A suspect device was also found outside his home - which later turned out to be a hoax, the court heard.
Mr Ward contended: "The information posted, the nature of the information and the speculation as to the current whereabouts of the plaintiff amounts to harassment of the plaintiff."
But Barry McKenna, for Mr McCloskey, questioned why Quinn's representatives never tried to approach his client to ask for any offending material to be taken down.
He added: "This plaintiff, I would say, does not come to court with clean hands.
"He has failed to disclose in respect of his rape conviction that he then was in breach of a sexual offences prevention order."
Counsel for Facebook, Peter Hopkins, argued that the legal move was disproportionate when balanced against users freedom of expression rights.
He also queried the extent of the risk Quinn claims to be under.
Following a further suggestion that only material directly related to the plaintiff should be removed, Mr Justice Horner adjourned the case for two weeks.
He directed Quinn's lawyers to write to Mr McCloskey's legal representatives setting out precisely what they are seeking.
The judge told the parties: "There are a whole lot of issues that arise here that haven't been looked at in any detail."