The MHRA chief Dr June Raine said more than 20 million doses of the AstraZeneca vaccine have now been given in the UK.
She said no effective vaccine or medicine is given without some risk.
Dr Raine added clinical trials allow people to find common side effects, but rare side effects only become clear when large numbers of people are being vaccinated.
She added it is a “strong possibility” that the vaccine is causing these extremely rare side effects.
The MHRA boss said “the evidence is firming up”, but “more work is needed to establish beyond all doubt” the vaccine has caused extremely rare blood clot”.