The European Medicines Authority (EMA) said five people who had the jab developed capillary leak syndrome on the continent.
The rare condition results in blood leaking from tiny vessels into muscles which can cause a sudden drop in blood pressure. If left untreated this can cause organ failure.
The AstraZeneca vaccine has been restricted to the over 30s in the UK after being linked to serious blood clots that can cause brain haemorrhage.
Nineteen people have died from rare blood clotting in the UK after taking the jab.
Countries around the world have restricted its use in younger people, including Australia and Germany.
The EMA said it was also reviewing reports of rare blood clots in the Johnson and Johnson vaccine, which uses the same technology as the AstraZeneca jab.
There have been four serious cases of clotting and low platelets in people who have taken the J&J vaccine.
Three occurred in the United States, the EMA said on Friday. One person has sadly died.
The regulator said is it not yet clear whether there is a causal association between either jab and any blood conditions.
A vaccination site in North Carolina stopped using J&J jab after 18 people had adverse reactions and another in Colorado said 11 people suffered side-effects such as “nausea and dizziness”.
The J&J jab has been earmarked for use in younger people in the UK because it is administered as a single dose.
J&J, which is based in the US, said it was aware of the reports of blood clots possibly related to its Covid vaccine and others, and was working with regulators to assess the data.
“At present, no clear causal relationship has been established between these rare events and the Janssen Covid-19 vaccine,” the company said in an emailed statement.
The UK has ordered 30 million doses of the J&J vaccine and it is currently under review by the regulator.
On Saturday a scientist advising the Government said any blot clots associated with the J&J vaccine are “extraordinarily rare events”.
Professor Peter Openshaw, a member of the Covid-19 clinical information network, told BBC Radio 4’s Today programme: “We still don’t know whether they are directly related and caused by the vaccine but it seems possible that they could be.
“It wouldn’t be surprising to find the J&J, the Janssen vaccine, also causes rare blood clots because it’s based on an adenovirus technology which is not that far away from the technology being used in the AstraZeneca vaccine.”
Asked if he is concerned it could undermine public confidence in coronavirus jabs, Prof Openshaw said: “These are extraordinarily rare events and there is no medicine that is going to be completely free of side effects but this is on the scale of the risk of adverse outcome you would expect if you get into a car and drive 250 miles, and many of us wouldn’t blink before taking that risk.”