He allegedly told his brother that if their niece, who is now a grown woman, went to police he would "beat her to a pulp" and then tie her up and make her watch him doing the same to her young daughter.
District Judge Liam McNally made an order banning publication of the man's name in order to protect the identity of his niece.
The 46-year-old man is charged with raping and indecently assaulting his niece "numerous times" between June 18, 1978, and June 18, 1980, when she was aged between four and six.
He is further charged that on June 15, and again on June 24, he attempted to pervert the course of justice by threatening to harm an injured party if she made a complaint to the police
A detective constable told the court he believed he could connect the man with the charges.
Outlining police objections to the man being released on bail, the officer explained that the alleged injured party came forward on July 3, and told police she wanted to report being raped by her uncle. On July 9, she made a statement alleging that between the ages of four and six she was repeatedly raped and indecently assaulted by her uncle. She could not be specific about the dates but said it happened every day, whether after school or at the weekend.
The detective said the woman had made the allegations to a member of her family 15 years ago.
He said that on June 15, the man asked his brother if he knew of the allegations and told him that if their niece went to the police he would "sort it out". In another conversation with his brother on June 24, he threatened that if the niece made the allegations he would beat her to a pulp and then tie her up and make her watch him do the same to her young daughter.
The officer told the court the brother was in no doubt the man "would carry out his threat and there would be a blood bath".
The man was arrested and denied all the allegations.
The detective said police were objecting to bail, given the man's previous history of violence and his previous convictions for violent offences and the fear he would carry out his threat and commit further offences.
He explained that the man was recently arrested for breaching his bail in relation to charges of assaulting a woman, making a threat to kill and possession of an offensive weapon. He was arrested in a pub in breach of a condition of his bail, forbidding him from entering licensed premises.
The detective told the court he was aware the man had an alcohol problem
The District Judge said that if the man was just facing the rape and indecent assault charges he would get bail because they were historic. However, there was "fairly strong evidence" from his brother that he threatened to do damage to his relatives and he had a record of violence.
Defence solicitor, Mr. Niall Bogue, said the man agreed that he had spoken to his brother but denied any allegations of making threats towards the injured party.
The detective confirmed: "He stated that he didn't make any threats."
The officer also confirmed that there were "issues" between the brothers but said there was no "vendetta".
After reading the brother's statement of evidence, the District Judge told the man: "This has been a very close run matter."
He released him on £1,000 bail, with a surety of £2,000, on condition that he resides at an address specified, does not enter licensed premises and is not under the influence of alcohol in public. He is also banned from having any contact with his brother, niece or any other witnesses in the case.
The District Judge warned the man that if he broke any of the conditions he would remain in custody until his trial.
The case was adjourned to Fermanagh Court on August 6.