"More cases are expected," the Oslo Municipality said in a statement.

"Effective tracing is being done to limit transmission routes and prevent major outbreaks."

The Norwegian Institute of Public Health said that those affected live in Oslo and surrounding municipalities, and "the infection detection team in Oslo has contacted the municipalities concerned to start infection detection".

The government agency said that there was "a high vaccination coverage" in the group, adding that overall "more than 50 cases" have been recorded in Norway.

The country's first two cases were announced Monday.

On Wednesday the city of Oslo urged people who visited two restaurants in the capital to be tested.

One reportedly was where the Christmas party was held.

Much remains unknown about the new variant, including whether it is more contagious, as some health authorities suspect, whether it makes people more seriously ill, and whether it can thwart vaccines.

It is customary in Scandinavia for companies, associations and individuals to hold Christmas parties in the weeks leading up to Christmas eve.

Much remains unknown about the new variant, including whether it is more contagious, as some health authorities suspect, whether it makes people more seriously ill, and whether it can thwart vaccines.

In response to Omicron, the Norwegian government said new national and regional restrictions would take effect on Friday.

Norwegian Prime Minister Jonas Gahr Stoere said the strictest measures were regional and would apply to Oslo — a city of nearly 700,000 — and surrounding municipalities.

He said they included working from home when possible, a 100-person attendance limit at private indoor events in public places or rented venues, and restaurants and bars having to register patrons.

Nationally, anyone entering Norway must be tested within 24 hours, either at the border, at a public test station or by self-test.

If a rapid test comes back positive, a traveller must take a PCR test within 24 hours, the government said.

"It is likely that the Omicron variant will spread in Norway, and that is why the government believes in stricter measures," Mr Gahr Stoere said.

Health Minister Ingvild Kjerkol said the situation was "worrying" and "we now pull the brake".

On Tuesday, Norway recommended the use of face masks on public transportation and in shops and shopping centres.

"We still have to keep our distance to get control of the spread of infection, but that does not mean that we cannot have good contact with each other," Mr Gahr Stoere said.