PST made the announcement at a press conference at 6pm on Thursday in Oslo.
The Norwegian Police Security Service said its evaluation showed no additional information to justify a specified threat to the country.
The police therefore continued its downgrading of the increased alert to a level in line with PST's last safety evaluation level from February.
The threat level was upgraded on Thursday 24th July after information pointed at a specific and imminent threat against Norway.
PST chief Benedicte Bjørnland said to NTB: "We have gathered the whole information picture that leads us to state a terror attack will not happen."
When PST sounded the alarm last week it was because they received information that a group of people was on its way from Syria to Europe. The intention was supposedly to carry out a terror attack and Norway was a possible target.
Bjørnland said: "The information on the threat was not verified. We did not know whether it was completely or partly correct. Nor was there any information on where, how, or why a possible terror strike would be committed."
The PST chief thinks that the threat is now significantly reduced. Bjørnland said: "The probability that the original information is correct is reduced. That means the threat of a near-future terror attack in Norway is reduced."
She added: "A possible effect of making the threat public could be that a terror attack has been prevented, but I guess we will never have an answer to that."
But Bjørnland added that the general danger of a terror attack and politically motivated violence still is present. She said: "Our democratic society is vulnerable, and even though the actual threat is reduced we are confronted with a significant remaining risk."
When PST chose to tell the public about the threat, it was in part because they had judged that it was necessary to place armed police on the streets.
Police director Odd Reidar Humlegård said: "The most visible measures were more uniformed and armed police, and our evaluation was that it was impossible not to inform society about the situation.
Humlegård confirmed the police will now reduce the alert to the same level as it has been since PST announced its last general threat evaluation this winter.