Denmark's navy says that Madsen's privately built submarine that had been feared missing in Danish waters has been found and the crew is safe.
FILE - This is a April 30 2008 file photo of submarine owner Peter Madsenstands inside the vessel.
Madsen claims he was the only one on board at the time, and that he dropped Miss Wall off at the mouth of the harbour shortly after 10pm the previous night.
Mr Madsen, an entrepreneur, artist, submarine builder and aerospace engineer, went before a judge yesterday for preliminary questioning. He is "willing to cooperate" and hasn't decided whether to appeal the detention ruling, Hald Engmark said.
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".
Ms Wall, who lived in the U.S. and China, studied at the Sorbonne university in Paris, the London School of Economics and at Columbia University in NY.
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.
He denies any involvement in the disappearance of 30-year-old Kim Wall who had been on board the 60ft-long vessel before it sank.
Mr Madsen initially said that he dropped Ms Wall off before it sank but police say he has now changed his statement - although they have not said what to.
Kristian Isbak, who had responded to the Navy's call to help locate the ship on Friday, told The Associated Press he first spotted Madsen standing wearing his trademark military fatigues in the submarine's tower while it was still afloat.
Before his arrest, Madsen told TV2 that the submarine sank when a minor ballast problem rapidly escalated and sunk the boat.
An unidentified woman stands in the tower of the private submarine "UC3 Nautilus" pictured in Copenhagen Harbor, Denmark August 11, 2017.
Before the hearing was closed, the courtroom was packed with Danish and Swedish reporters and Madsen's relatives. Madsen said he had left her on the end of the Refshaleøen island at around 2030 GMT, according to police. He has denied responsibility for the 30-year-old woman's fate, saying she disembarked earlier.
Her boyfriend alerted police early Friday that she had not returned home as planned.
"It appears as though it was a deliberate action that caused the sub to sink", Mr. Moller said.