Mr. Madsen, 46, has been arrested on suspicion of negligent manslaughter after being rescued from the sea on Friday, August 11.
The Nautilus, the largest privately-owned submarine in the world, started taking on water after going out on a trial journey. But the whereabouts of Ms. Wall, a 30-year-old freelance journalist who was writing an article about him and the sub, remains a mystery. Mr. Madsen has claimed he dropped her off near a restaurant on Refshale Island in Copenhagen harbor on Thursday (August 10) evening.
We hope she is found safe!— Tom Walker (@TomWalk94849237) August 12, 2017
But the Danish police believe she was on board the Nautilus when it began to sink.
The submarine was recovered from the seabed in Koge Bay on Sunday (August 13) and Ms. Wall's body was not inside it, but it is feared she may have managed to get out and then drowned. Her family and friends have resorted to social media in an effort to find her.
Under Danish law Mr. Madsen can be held in custody for 24 days before being charged. The incident could join the list of the strangest submarine mysteries in the world.
"At the moment we don't know where she is or if she's alive. That means police and rescue workers have to look both on land and at sea," said Ole Thiell Sorensen from the Danish police.
"In most cases we work with looking for survivors and that's hard enough. Looking for a dead person is even more difficult because you cannot use thermal cameras," he said.
Kristian Isbak said he saw the Nautilus sink on Friday morning.
"We realized that it was Peter Madsen's submarine. A man sat in the tower, he climbed down and then up into the tower again. There was a powerful pressure wave around the submarine. It began to sink. Madsen stood quite calmly in the tower. When the submarine had sunk so much that he could swim, it only took 10-15 seconds, Madsen leaped into the water and paddled to a rescue boat," said Mr. Isbak.
Mr. Madsen gave a thumbs-up to journalists when was brought ashore and said he was "sad" to have lost the Nautilus, but made no mention of Ms. Wall.
Several people have posted pictures of Mr. Madsen and Ms. Wall in the conning tower of the sub together, but it is not clear whether they were taken on Thursday or Friday.
"I was out on a rehearsal trip, tinkering with different things in the submarine. Then a defect happened with a ballast tank which wasn't that serious, until I tried to repair it. Then it suddenly became very serious," said Mr. Madsen.
Ms. Wall alternated her life between New York and Beijing, but had worked all over the world for a variety of magazines and newspapers.
Mr. Madsen built the Nautilus in 2008 with the help of a crowdfunding appeal and is currently engaged in a bid to put a man- or woman — into space.