"There have been both ransom demands and serious threats", Tommy Brøske, the police inspector leading the investigation, said at a press conference in Oslo on Wednesday morning.
Anne-Elisabeth Falkevik Hagen, 68, has been missing since October 31, chief investigator Tommy Broeske said on Wednesday, with police saying she was abducted "against her will".
Tommy Broske at the Eastern Police District said the way Mrs Falkevik Hagen was abducted suggested "that these are professional offenders".
Her husband Tom Hagen, a real estate investor and owner of power facilities, is among the wealthiest people in Norway, boasting a total wealth of about $2 billion.
Mrs Hagen is married to Tom Hagen, a businessman with an estimated fortune of 1.7bn Norwegian krone (€174m; £156m) made in the real estate and energy industries.
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It is suspected that she has been kidnapped, and someone claiming to be the kidnapper has in a letter demanded that a ransom of nine million euros (approximately $10.3 million) is to be paid in the cryptocurrency monero. Mr Broeske declined to comment other than saying "the threats (in the note) were of a very serious character". This has reportedly prevented the police from searching for the kidnappers as aggressively as they would normally have done, while also limiting their ability to gather evidence in the vicinity of the couple's residence outside of Oslo.
Due to the sensitivity of the operation, the police have been forced to keep an extremely low profile while investigating the case. "That is all I'd say", he added.
Mr Broeske said "those behind have chosen to communicate digitally and we have had no other type of contact". Police had urged the family not to pay any ransom.
Norwegian authorities are working together with Europol and Interpol on the case.
"Our main theory is that the victim was kidnapped by unidentified perpetrators at her home" in Lorenskog, about 20 kilometres (12 miles) from Oslo, he said.