A person carrying the coronavirus in Norway contaminates now on average 0.7 other individuals, Bent Hoeie told a news conference on Monday.

The government's goal had been to limit the spread to maximum one other person.

"Before we implemented tough restrictions, every contaminated person in Norway infected 2.5 other individuals on average," Hoeie said.

"If this development had been allowed to continue, we would probably have been in the same situation that we have seen in some countries in Europe."

The Norwegian government announced three weeks ago emergency shutdowns of many public and private institutions, including schools and kindergartens, sending the economy into a tailspin and triggering hundreds of thousands of lay-offs.

The government will decide on Wednesday whether to extend the restrictions beyond mid-April.

It was not immediately clear which measures could be lifted, nor when they would be.

Local authorities in the capital Oslo and Trondheim, Norway's third-largest city, have already said they will not reopen schools and nurseries by mid-April because they needed more time to prepare.

The Norwegian Institute of Public Health (FHI) said on Monday the number of coronavirus cases in the country stood at 5755 people, with 59 deaths.

The FHI also estimated for the first time on Monday that about 14,000 people in total may be carrying the virus in Norway, or 0.26 per cent of the population.

"It is good news. It shows the restrictions have worked," Camilla Stoltenberg, the head of the institute, told public broadcaster NRK. "(But) we don't know which specific measures worked."

Australian Associated Press