Peter Madsen was arrested Friday on preliminary manslaughter charges after his 40-ton, almost 18-meter-long (60-foot-long) submarine sank off Denmark's eastern coast.
The 30-year-old Sweden-born freelance journalist had studied at the Sorbonne university in Paris, the London School of Economics and at Columbia University in NY where she graduated with a master's degree in journalism in 2013.
He is now being held on preliminary manslaughter charges with a judge set to rule on Saturday whether he must remain in detention while investigations are carried out. "I would very much like to express myself", he said after the preliminary charges were read.
In a statement to Swedish paper Aftonbladet, Ms Wall's family said: "It is with great dismay we received the message that Kim is missing".
Miss Wall is a freelance journalist who graduated with a masters from Columbia University before going on to write about identity, gender, pop-culture, social justice and foreign policy.
The submarine's Danish inventor, Peter Madsen, is being held on suspicion of manslaughter in Wall's disappearance.
Before his arrest, Madsen told TV2 that the submarine sank when a minor ballast problem rapidly escalated and sunk the boat.
The 40-ton, almost 18-meter-long (60-foot-long) vessel has been described as the largest privately built submarine of its kind.
"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 told The Associated Press. The submarine, UC3 Nautilus, is one of three constructed by Madsen.
Isbak says he then saw Madsen swim over to another private boat.
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.
Madsen told authorities he had dropped her off back at their departure point at about 10:30 p.m.
A Danish court has ordered the owner of an amateur-built submarine be held in pre-trial detention for 24 days while authorities investigate the mystery disappearance of a Swedish journalist who was aboard the vessel before it sank. He has denied responsibility for the 30-year-old woman's fate, saying she disembarked earlier.
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 has denied wrongdoing and said that he dropped Wall-who was reported to be the only other person on board the submarine with him-off on an island close to Copenhagen Thursday night before the submarine sank, according to AP reports.