Judge Kari Soerensen announced the ruling after a two-hour custody hearing held behind closed doors. He is "willing to cooperate" and hasn't decided whether to appeal the detention ruling, Hald Engmark said.
Copenhagen's Deputy Police Inspector Jens Moller Jensen says investigators are looking for witnesses who may have seen the woman after the time Madsen reported she disembarked.
Kim Wall's family said in statement emailed to The Associated Press on Saturday, "It is with great dismay that we received the news that Kim went missing during an assignment in Denmark". She has written for the New York Times, The Guardian, the South China Morning Post and Vice Magazine, among others.
The journalist was born in Sweden and studied at the London School of Economics, Columbia University in NY and the Sorbonne in Paris.
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The submarine's Danish inventor, Peter Madsen, is being held on suspicion of manslaughter in Wall's disappearance.
Madsen said "a minor problem with a ballast tank turned into a major issue" that ultimately caused the submarine to sink.
The vessel - the biggest privately made sub ever made when built in 2008 - was located in a bay in Kge, some 50kms from the Danish capital, where the submarine had suddenly sunk shortly before midday.
"He then climbed down inside the submarine and there was then some kind of air flow coming up and the submarine started to sink", Isbak said. The submarine, UC3 Nautilus, is one of three constructed by Madsen.
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Isbak says he then saw Madsen swim over to another private boat.
Mr Madsen was rescued, but there was no trace of the woman.
Madsen's company RML Spacelab is seeking to send people into space and is developing a rocket, floating launch pad and astronaut testing machine, its website says.
Danish police have charged Peter Madsen, 46, with manslaughter following the disappearance of a female Swedish journalist who boarded his submarine, the Nautilus, at Refshaleøen in Copenhagen on Thursday evening.
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The delegation asked the premier for their political freedom, and demanded to get their closed offices reopened. During the meeting, issues concerning law and order and development came under discussion.
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 Navy said it was spotted sailing but then sank. The inventor told authorities Friday that he dropped Wall off on an island in Copenhagen's harbor before the vessel sank.