PM Jens Stoltenberg described the situation as "very serious".
The bomb was followed by a fatal shooting incident near Oslo at a youth meeting of the Labour Party, which Mr Stoltenberg leads.
Norwegian media said at least four people were killed when a man opened fire indiscriminately.
Police said the suspected gunman had been arrested, TV2 reported.
No group has said they carried out the attacks but police say they believe them to be linked.
Hours after the bomb struck Oslo, officials said some people were still inside the damaged buildings, some of which were on fire.
Television footage from the government quarter showed rubble and glass from shattered windows in the streets and smoke from the fires drifting across the city. Read more.