From Wednesday, people living with a Covid-19 patient will be required to self-isolate until they test negative for Covid-19.
This rule will be binding on all adults, regardless of vaccination status, but only a recommendation for children, Stere said.
People with Covid-19 will need to be quarantined for five days.
The Prime Minister emphasized that the pandemic was not over, but was entering a new phase. You have to get used to living with and controlling the coronavirus, said Stere.
He acknowledged that the new South African, or omicron, form of Covid-19 had created insecurity, but the authorities and government were closely monitoring the situation.
Stere also called on citizens to go vaccinated against Covid-19 and receive a booster vaccine, if one is offered.
Norway has been doing quite well in the fight against the pandemic for a long time and lifted most of its restrictions in September.
However, as the number of cases rose again, the government introduced new restrictions in mid-November.
According to the European Center for Disease Prevention and Control (ECDC), the seven-day cumulative number of infections per 100,000 population in Norway is currently around 480.