Speaking on his radio programme Radio 1, Adaktusson cited credible sources from Eritrea's opposition movement as indicating that Isaak is no longer in the Eira Eiro prison because he is dead.
However, the information hasn't been officially confirmed.
“We have no information to confirm either that he has been moved or that he is dead,” Anna Backlund at the Swedish foreign ministry's informaion department told The Local.
The foreign ministry will now make a thorough investigation whether there is any information from within the ministry organisation indicating that there is any basis to the rumours about Isaak's death.
Mehari Abraham, an Eritrean-exile commentator and journalist at TV-Zete in Stockholm is one who believes that Isaak is no longer alive.
"It's very credible information but it's extremely hard to get it confirmed," he told the TT news agency.
While the information hasn't been officially confirmed, the sources claiming that Isaak is no long in the prison have been right about ten previous deaths.
However, Leif Öbrink, chair of the Free Dawit Isaak campaign, was highly critical of the spreading of the information about Isaak's supposed death, calling it “speculation”.
“This has been circulating for several weeks, this information. No one believes it. I think it's totally wrong to go out with it,” he told TT, questioning the motives of Adaktusson and Abraham.
“What does he want? To discredit the regime? One has to bear such things in mind,” Öbrink said of Abraham.
“This is sensationalism from Adaktusson's side.”
Isaak's daughter Bethlehem also cast doubt on reports that her father was dead.
“We don't believe this information,” she told the Expressen newspaper.
Arhe Hamednace, a Social Democrat MP of Eritrean decent, is concerned the reports may be accurate.
He explained on the radio programme that he received reports about Isaak about two months ago.
“There were some people who called me. One high-placed person that works in an organistation with international contacts called me and said that 'we have information, we've heard that Dawit is no longer alive',” said Hamednaca.
He later contacted sources in his own network in Eritrea but failed to get the information confirmed.
“But we know how this regime acts. No one who is a high-ranking politician or government critic has come out alove from this prison,” he said on Adaktusson's programme.
Thomas Mattsson, editor of the Expressen newspaper, which has been at the centre of the movement to draw attention to Isaak's case and win his freedom, said the report that the imprisoned journalist may be dead was “terrible news”.
“Terrible if it's true. Nearly as terrible if it's not true – Dawit Isaak has a wife and three children and it's with them that our thoughts go now. I really hope this is a misunderstanding, a mistake.”