The group posted pictures of two men, a Norwegian graduate student and a Chinese consultant, in the latest issue of its online magazine Dabiq, giving a telegram number under each for “whoever would like to pay the ransom for his release and transfer”.
The ransom note for the Ole Johan Grimsgaard-Ofstad, a student at the Norwegian University of Science and Technology, comes at the end of the magazine under the headline “Norwegian Prisoner for sale”.
Norwegian Prime Minister Erna Solberg cancelled a scheduled appearance on Norway's NRK channel after the latest issue of Dabiq Magazine was published on Wednesday evening.
"IS's brutality knows no borders and now they have claimed one of my own," she said in an emergency press conference. "In late January we learned of the possible kidnap of a Norwegian citizen. He has since been held by different kidnappers, but there is reason to believe he is now held by IS."
She said that while Norway aimed to secure his safe release, it was not willing to buy him back from the terror group.
"Norway does not pay ransom money," she said.
Grimsgaard-Ofstad posted on Facebook in January that he had arrived in the Syrian town of Idlib, although why he was there has yet to be determined. His Facebook page includes many photographs of ancient sculptures and ruins.
“I am in Idlib, Syria. Going to Hama tomorrow. I finally made it,” he wrote.
Idlib was at in January controlled by the Syrian government but was overrun by the Islamist coalition Jaish al-Fatah in March.
The Chinese man was advertised in the magazine as Fan Jinghui, 50, a freelance consultant from Beijing.