Peter Madsen fled the Herstedvester Prison brandishing a "pistol-like object" on Tuesday, but was apprehended a short time later.
"There is no doubt that he murdered Kim Wall on purpose and that he had a sexual motive," said the prosecutor.
A Danish Navy officer says it can't have happened the way Madsen says.
The prosecutor tried to establish a sexual motive for the murder.
A charge sheet alleged that Wall's murder had been premeditated because Madsen brought "tools" he normally did not take on submarine trips.
New post-mortem evidence showed Wall was stabbed multiple times immediately before or around the time of her death.
Wall disappeared on August 10 after boarding the private submarine of Peter Madsen.