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.
Police probing the mysterious disappearance of a Swedish journalist last seen boarding a homemade submarine said Monday its Danish inventor, accused of manslaughter, deliberately sank the craft.
Ms Wall was not found inside the submarine after it was raised and transported for investigation on Saturday.
The vessel was recovered on Saturday from Koge Bay, south of Copenhagen, where it had been lying at a depth of seven metres, and taken into harbour. On Sunday, they said Madsen had given another explanation, but declined to elaborate.
He has been charged with negligent manslaughter "for having killed in an unknown way and in an unknown place Kim Isabell Frerika Wall of Sweden sometime after Thursday 5pm", according to the public prosecutor, Louise Pedersen.
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She said she didn't contact police in order to protect her daughter, saying she didn't want the incident to "define her life". She listened closely and took notes during Mueller's testimony; and is expected to take the stand herself in the coming days.
On Friday morning, the Danish police located Peter Madsen aboard Nautilus - without Wall.
A couple of hours before the boat was reported missing, a major commercial ship was close to a collision with Nautilus; adding to the suspicions about what really happened between Thursday evening and Friday morning. Found empty, the vessel is now undergoing technical investigation by the police - in conjunction with extensive search efforts around the waters of Öresund to find Wall.
Madsen, who was described in a 2014 book as "Denmark's Do-It-Yourself Astronaut", had wanted to launch himself into the space race before building the crowd-funded Nautilus, the biggest privately-made one ever when he built it in 2008.
After his submarine sank at around 11:00am on Friday, Madsen alone was brought to shore on board a private boat. "But I guess that was pretty good because I otherwise still would have been down there".
Madsen, an entrepreneur known as an artist, submarine builder, and aerospace engineer, went before a judge on Saturday behind closed doors for preliminary questioning. It was built to carry eight people.
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