A cyclist found a torso — missing its arms, legs and head — on Monday, and the remains were identified on Wednesday as Ms. Wall’s.
The police are still looking for the rest of the victim’s body. On Thursday, the police said they had recovered what could be a body part from a location in the sea north of Falsterbo in Sweden, southeast of Copenhagen, across Oresund, the strait that separates Denmark and Sweden.
In a statement, they said that a forensic examination would determine whether the body part, originally found by bystander, belonged to Ms. Wall.
The torso was found without clothing, and the police asked locals to look out for the apparel Ms. Wall was wearing when she was last seen: a bright orange sweatshirt, a black-and-white flowered skirt and white shoes.
At Mr. Madsen’s next court appearance, on Sept. 5, prosecutors plan to request that he remain in detention. They will most likely request a psychiatric evaluation of Mr. Madsen, a routine measure in cases involving the most serious crimes.
The case has riveted Scandinavia, where Mr. Madsen is well known as a quixotic if mercurial innovator, and it has plunged Ms. Wall’s friends and relatives into grief.
Malin Angelica Franzén, a friend from southern Sweden, where Ms. Wall grew up, declined an interview request but guided a reporter to a Facebook post, in which she wrote: “Just three weeks ago she sat here in our sofa and talked about her new house in China, showed pictures of Chinese T-shirts with inappropriate English texts, and demonstrated translation apps. Talked about love, about the myriad stories to tell, about the future, about her life.”
Ms. Franzén remembered her friend — who was a graduate of the London School of Economics and had two master’s degrees from Columbia University — as not only courageous, but also modest.
“To lose her is not just to lose a friend, but a source of inspiration,” she wrote.
Caterina Clerici, who met Ms. Wall when they took the entrance examination for Columbia Journalism School, expressed shock that the journalist, who had reported from Cuba, Sri Lanka and Uganda and had written for The New York Times, among many publications, died so close to home.
“She was never reckless,” Ms. Clerici said. “She never did anything stupid. She knew what she was doing. She was very well traveled. She had a lot of experience even though she was fairly young.”