The man, said by police to be aged around 20, was arrested after a bus driver heard him late on Tuesday make threatening statements on the phone, implying he might attack the parliament building.
Police cordoned off the parliament and Oslo town hall from Tuesday night until the man was arrested at midday Wednesday.
The suspect was not named but Norwegian media said he was a 27-year-old with links to the far-right Norwegian Defence League.
"This person is known by our services," an Oslo police spokesman, Johan Fredriksen, told a news conference. "He has already made threats in the past."
The police said they had found a jacket - without saying whether it was bullet-proof - along with a gas pistol and a bag full of clothes.
The spokesman said the vigorous response by the authorities was justified by vigilance needed nearly 18 months after Anders Behring Breivik killed a
total of 77 people on July 22, 2011.