PM Jens Stoltenberg described the situation as "very serious".
The bomb was followed by a shooting incident near Oslo at a youth meeting of the Labour Party, which Mr Stoltenberg leads.
Unconfirmed reports said a man dressed as a police officer had opened fire indiscriminately, injuring five.
No group has said they carried out the attacks.
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 - smoke was rising from some buildings where fires were burning. The wreckage of at least one car was on one street.
Continue reading the main story
Smoke in downtown Oslo
All roads into the city centre have been closed, said national broadcaster NRK, and security officials evacuated people from the area, fearing another blast.
Mr Stoltenberg, in a telephone call to Norwegian television, said all government ministers were believed to be safe.[/p]
Personally, I'm a bit shocked something like this would happen again in Scandinavia, more so Oslo. Although a bombing has happened recently in Sweden (a failed one), this one is of particular big magnitude.