Any adverse reactions to the vaccine are publicly reported to and recorded on the Centre for Adverse Reaction Monitoring website.
"It is a smaller rate of reactions than almost any other vaccine we use," Hipkins said.
The top 10 most frequently reported adverse events after being vaccinated are, in order, headache, dizziness, nausea, fever, lethargy, injection site pain, musculoskeletal pain, feeling of body temperature change, numbness and chest discomfort.
There were "only a handful of people" who had reported very severe reactions after getting the vaccines; while a larger number of people had displayed more minor reactions, such as a cough or sore arm, he said.
In the latest Safety Report, published on the Medsafe website on June 30, 451 new adverse events following immunisation were reported up to and including June 5 of this year.
Of those reports, 428 were dubbed to be "non-serious" and 23 were regarded as serious.
Two of the serious reports included in the latest update were deaths.
No safety concerns with the vaccine were raised by the reports.
A summary given about the reported deaths said that up to and including June 5 of this year, a total of eight deaths were reported after the administration of the Comirnaty vaccine (also known as Pfizer vaccine).
"Following medical assessments by [Centre for Adverse Reaction Monitoring] and Medsafe, it has been determined that four of these deaths are unlikely related to the Covid-19 vaccine.
"Two deaths could not be assessed due to insufficient information [and] two cases are still under investigation."
The report went on to point out that "by chance," some people will experience new illnesses or die from a pre-existing condition shortly after vaccination - particularly if someone is elderly.
"Therefore, part of our review process includes comparing natural death rates to observed death rates following vaccination, to determine if there are any specific trends or patterns that might indicate a vaccine safety concern."
The report said that there are currently no indications to suggest that the vaccine caused the deaths reported.