The transcript, however, shows that Mr. Durst discussed his heath issues — surgery for cancer of the esophagus and hydrocephalus, a buildup of fluid in the brain — while appearing alert and responsive. Mr. Durst reeled off various phone numbers and addresses and, at different points, declined to answer Mr. Lewin’s questions.

He was advised of his right to counsel, according to the transcript, and the fact that anything he said could be used against him. But he continued talking, and toward the end of the interrogation, Mr. Durst told Mr. Lewin, “I’m very willing to talk to you.”

The defense is also opposing Mr. Lewin’s motion to have a special master appointed to determine whether there were any materials protected by attorney-client privilege among a mountain of evidence seized by the authorities from Mr. Durst’s apartment in Houston, his hotel room in New Orleans, and a home in New York where Mr. Durst had 63 cartons of court records, credit card receipts, photographs and family business papers.

The defense, in papers it filed last Thursday in Los Angeles, argues that the “documents were obtained through illegal searches and seizures, which included lack of probable causes,” and should be disallowed as evidence.

Dick DeGuerin, who leads Mr. Durst’s defense team, said those issues and others would be addressed in court on Wednesday.

Mr. Durst is worth an estimated $100 million and has long been estranged from his family, which owns more than a dozen Manhattan skyscrapers. He has been under scrutiny by investigators in three states for more than three decades, suspected of murdering his wife and Ms. Berman. In 2003, he was acquitted on charges of murdering a neighbor in Galveston, Tex., despite his graphic testimony of how he cut up the man’s body, threw the parts in Galveston Bay and later fled Texas with the authorities in pursuit.