“There’s no doubt in my mind that if he had the opportunity to kill me, he would,” Douglas Durst said.

Yet it is not worries about a physical threat that has prompted Douglas to speak now, he said, but what he believes will be a violent broadside against the family name and history: In coming weeks, HBO plans to broadcast a six-part documentary, “The Jinx: The Life and Deaths of Robert Durst.” It draws on 25 hours of interviews with Robert Durst.

Douglas Durst, 70, has not seen it. Nor did he agree to be interviewed by the filmmakers, Andrew Jarecki and Marc Smerling, despite repeated entreaties. Nevertheless, he believes that the series will be rooted in an untrustworthy source.

“Bob is incapable of telling the truth,” Douglas Durst said. “He is a true psychopath, beyond any emotions. That’s why he does things, so he can experience the emotions that other people have vicariously. Because he has absolutely none of his own.”

Through his lawyer, Robert Durst was invited to discuss the matters raised by his brother, but declined. “Bob appreciates the opportunity to speak with you, but he’s not going to do so at this time,” the lawyer, Steven M. Rabinowitz, wrote in an email.

ROBERT DURST has had improbable success in mounting his version of reality at critical moments. He was able to convince a Texas jury that he was not legally responsible for the death of the man whose body he dismembered in 2001. Caught on videotape in 2012 and 2013 lurking around the homes of Durst family members in Manhattan from which he had been barred, he and his lawyer were still able to persuade a judge last month to acquit him of trespass by maintaining that Mr. Durst did not know which specific properties were owned by the family. Afterward, he told Charles V. Bagli of The New York Times that he had once managed those very buildings.