"We are not alarmed by this. It is quite clear that these vaccines have very little risk, with a small exception for the frailest patients," Steinar Madsen, medical director with the agency, told Norwegian broadcaster NRK.
"Doctors must now carefully consider who should be vaccinated. Those who are very frail and at the very end of life can be vaccinated after an individual assessment," he added.
Earlier this week, the Norwegian Institute of Public Health said that "any side effects of the vaccine will be outweighed by a reduced risk of becoming seriously ill with Covid-19 for elderly, frail people".
It added that "for very frail patients and terminally ill patients, a careful balance of benefit versus disadvantage of vaccination is recommended".
In its report, the Norwegian Medicines Agency said that 21 women and eight men had side effects.
Beside those who died, the agency said nine had serious side effects without a fatal consequence and seven had less serious side effects. The nine patients had allergic reactions, strong discomfort and severe fever, while the less serious side effects included severe pain at the injection site.
Overall, Norway has seen 57,279 Covid cases and reported 511 deaths.
Across the world, officials expect deaths and other severe side effects to be reported after any mass vaccination campaign given the huge numbers of people involved. But determining whether or not the vaccine caused deaths can be very challenging and requires that all other potential causes be ruled out first.
The United Kingdom and the United States have also reported a number of cases of side effects that had fatal consequences.
The European Medicines Agency said on Saturday that it will receive and consider monthly safety reports from companies authorised to sell vaccines, starting in January with the Pfizer jab.
