The powerful early morning blast on Sunday from an improvised explosive device (IED) damaged the entrance to the embassy's consular section but caused no injuries, Norwegian authorities have said.
The three suspects, all in their 20s, are Norwegian citizens with a family background from Iraq, police said.
"They are suspected of a terror bombing," Police Attorney Christian Hatlo told reporters.
"We believe they detonated a powerful bomb at the US embassy with the intention of taking lives or causing significant damage," Hatlo said, adding that none of the suspects had so far been interrogated.
Reuters could not immediately establish whether the three admitted to any crimes or maintained their innocence.
Images of one of the suspects released by police on Monday showed a hooded person, whose face was not visible, wearing dark clothes and carrying a bag or rucksack.
Investigators on Monday said one hypothesis was that the incident was "an act of terrorism" linked to the war in the Middle East but that other possible motives were also being explored.
Police are investigating whether the bombing was done on behalf of another country although other possible motives were also being explored, Hatlo said.
European countries has been on alert for possible attacks as the US and Israel conduct air strikes on Iran and Iran launches drone and missile attacks on Israel and US targets in the Middle East.
On Monday, a synagogue in the Belgian city of Liege was damaged by a blast that authorities called an anti-Semitic attack.
It was not clear who was behind it.
