The blast caused massive damage to the building housing Mr Stoltenberg's office, as well as nearby ministries and other buildings. Police are still searching for more bodies or people who may be trapped.
Anders Behring Breivik, a Norwegian of 32 alleged to hold extreme nationalist views, has been charged with both attacks and is being questioned.
Flags are flying at half-mast and security has been stepped up across Norway.
Flowers and candles for the victims of the twin attacks are set out in central Oslo.
The horror of Norway's island shooting emerged overnight - police now say 84 bodies have been found. Many more people were injured.