Norwegian health officials established no link between Pfizer/BioNTech's Covid-19 vaccine and 33 deaths among elderly people who received their first dose.
Authorities recommended that doctors consider the overall health of frail patients before carrying out inoculations, after analysis found advanced age and serious illness were major factors in some of the deaths.
A leading British immunologist welcomed Norway's investigation but said the public should maintain confidence in the vaccine.
Norway registered the 33 deaths in the weeks following the start of its vaccination campaign in late-December.
Camilla Stoltenberg, director general of the Norwegian Institute of Public Health, said all 13 cases that were analysed involved elderly patients who were frail and had serious illnesses.
"It is important to remember that on average about 45 people die every day at nursing homes in Norway, so it's not a given that this represents any excess mortality or that they are related to the vaccines," she said.
Prof Peter Openshaw from Imperial College London said the deaths should not unduly affect public confidence in the vaccine.
"Not at all. But it's very important that it's property investigated," he told The National.
Norwegian officials said doctors should consider whether patients who were frail or terminally ill should receive the vaccine on a case-by-case basis.
"It's not impossible that some of those who have gotten the vaccine are so frail that maybe you should have reconsidered and not given them the vaccine, because they are so sick that they might have become worse from the normal side effects as the body reacts and builds up immunity," Ms Stoltenberg said.
The Norwegian Medicines Agency said last week that normal side effects from the vaccine, such as fever and nausea, may have "contributed to a fatal outcome in some frail patients".
Several countries, including Norway's neighbours Denmark, Finland and Sweden, as well as Iceland, reported some post-vaccination deaths, although no direct link to the vaccine was established.
Pfizer and BioNTech said they were working with the Norwegian Medicines Agency to "gather all the relevant information".
They said Norway's vaccination campaign started with the elderly in care homes.
"Most of [the residents] are very elderly with underlying medical conditions and some of which are terminally ill," the companies said.
More than 48,000 people have been vaccinated against the virus in Norway so far.