Police spokesman Stefan Dangardt says no arrest has been made in Sweden.
Icelandic officials said it was unlikely Stefansson had to show a passport at the airport since he travelled within Europe's passport-free Schengen travel zone, but the plane ticket he used was under someone else's name. "We are sure of that".
An worldwide arrest warrant has been issued for the Stefansson.
According to Visir, a local news site, the Sogn prison was only 60 miles from Keflaviks airport. At the current prison, inmates are not restricted by fences and have access to amenities like Wi-Fi and phone service. The stolen equipment, which still is missing, has been valued at nearly $2 million.
Mr Stefansson was among 11 people arrested for allegedly stealing the powerful computers in a series of four burglaries in December and January in what is considered Iceland's biggest-ever heist.
Stefansson had been in custody since February.
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A passenger told national broadcaster RUV that the only notable thing about the flight from Keflavik appeared to be the presence of Ms Jakobsdottir, the 41-year-old Left-Green Movement leader.
Iceland's prime minister, Katrín Jakobsdóttir, was reportedly on the same flight as Stefansson on her way to meet India's prime minister in Stockholm on Tuesday.
The Prime Minister's presence, the witness said, was the only unusual thing about that flight.
The prison break is yet another twist in a criminal case without parallel on the peaceful island nation with a population of 340,000 and one of the world's lowest crime rates. Police commissioner Olafur Helgi Kjartansson told The Associated Press in March it was "a grand theft on a scale unseen before".
Police have arrested a total of 22 people, including a security guard, in connection with the heist.