Police said Peter Madsen, 46, was rescued on Friday after his 17-metre-long homemade submarine began taking on water south of Copenhagen. But he told police that he had dropped off the reporter, Kim Wall, at a remote Copenhagen island around three hours into the trip.
Deputy Insp Jens Moller Jensen said investigators were looking for witnesses who may have seen the woman after the time Madsen said she disembarked.
Hald Engmark says Madsen is "willing to cooperate" and hasn't decided whether to appeal the detention ruling.
Swedish police said later in the day they were investigating the whereabouts of a missing woman who had been on the submarine at some point.
"It is with a great concern that we, her family, received the news that Kim is missing after an interview with Peter Madsen in Denmark", the statement said.
According to a statement Wall's family shared with CPJ today, the 30-year-old Swedish-born journalist, who was based in NY and Beijing, was working on a story about inventor Peter Madsen when she went missing.
The journalist was born in Sweden and studied at the London School of Economics, Columbia University in NY and the Sorbonne in Paris.
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.
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Madsen said "a minor problem with a ballast tank. turned into a major issue" that ultimately caused the vessel - considered the largest privately-built submarine of its kind - to sink. "[He] came up again and stayed in the tower until water came into it".
Isbak says he then saw Madsen swim over to another private boat.
After his 18-meter-long vessel went down near Copenhagen he said the missing journalist - feared drowned - left him before it sank.
A judge is set to decide if the owner of an amateur-built submarine should be held in custody during an investigation into whether he is responsible for the disappearance of a Swedish woman who had been onboard his submarine that sank off Denmark's east coast.
Prosecutor Louise Pedersen said Madsen faces the preliminary manslaughter charge "for having killed in an unknown way and in an unknown place Kim Isabell Frerika Wall of Sweden sometime after Thursday 5 p.m".
Her partner raised the alarm in the early hours of Friday when she failed to return from the Nautilus vessel.
The Navy said the sub was seen sailing, but then sank shortly afterwards.