Danish police said on Saturday they were preparing to search a sunken submarine owned by Danish inventor Peter Madsen who has been charged with the inadvertent manslaughter of a journalist.
Nautilus, named after the ship from the classic science fiction novel Twenty Thousand Leagues Under the Sea, was built by Mr Madsen after raising $200,000 (£154,000) online.
Hald Engmark says Madsen is "willing to cooperate" and hasn't decided whether to appeal the detention ruling.
They described her as "160cm tall, 56kg, 30 years old, with reddish-brown hair and green eyes". Wall has not been reachable by phone since shortly after boarding Madsen's UC3 Nautilus submarine as part of an assignment for "Wired" magazine on Thursday evening.
In a statement to Swedish paper Aftonbladet, Ms Wall's family said: "It is with great dismay we received the message that Kim is missing".
The journalist was born in Sweden and studied at the London School of Economics, Columbia University in NY and the Sorbonne in Paris.
A look at her Facebook page reveals she has written stories all over the world for the likes of the New York Times and the Guardian.
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Friends, relatives and colleagues of Wall, who had been educated at Columbia University, Sorbonne and the London School of Economics, and worked as a freelance journalist, have bombarded social media with requests for information about her.
Kristian Isbak tells The Associated Press he had responded to the Navy's call to help locate the submarine on Friday when he spotted Madsen. He previously said he dropped her off on one of Copenhagen's harbor islands.
"We realized that it was Peter Madsen's submarine". Divers were initially unable to safely enter it.
Isbak says he then saw Madsen swim over to another private boat. The court decision follows Madsen's arrest yesterday on preliminary murder charges. He has denied responsibility for the 30-year-old woman's fate, saying she disembarked earlier. The inventor has denied wrongdoing and said that he dropped Wall-who was reported to be the only other person on board the submarine with him-off on an island close to Copenhagen Thursday night before the submarine sank, according to AP reports.
However, when she failed to return home later that day, her anxious boyfriend contacted the authorities, which led to a full-scale search for the submarine in the early hours.
The hearing starts at 1200 GMT.