Some municipalities are considering advising residents against travel to Oslo, according to newspaper VG.
49 people tested positive for Covid-19 in the city on Tuesday, NRK reports, an increase of 5 from the previous day.
Oslo Municipality has registered a total of 547 new cases over the last 14 days according to VG's running total of national database figures.
Lunner and Vestby are among municipalities considering a recommendation to avoid the capital.
“I see non-essential travel to Oslo as not very wise,” Vestby Municipality spokesperson Tom Ludvigsen told VG.
Oslo announced on Monday new measures intended at reducing infections, including a temporary ban on indoor events with over 50 participants if the participants are not seated and a mandatory requirement for face mask use on congested public transport.
The latter measure is now being considered by outlying municipalities Nesodden, Lilletrøm, Rælingen, Lunner, Gjerdrum and Gran, VG writes.
A number of the municipalities were engaged in discussion over potential measure on Tuesday with confirmation of any decisions expected to follow.
Any decisions will come against a background of easing national restrictions. Prime Minister Solberg announced on Wednesday that a ban on serving alcohol after midnight would be lifted from October 12th, while outdoor events will be allowed attendances of up to 600 people.