The EMA's expert committee on medicine safety, Mrs Cooke said, had found that "the vaccine is not associated with an increase in the overall risk of... blood clots".
But the EMA, she added, could not rule out definitively a link between the vaccine and a "small number of cases of rare and unusual but very serious clotting disorders".
Therefore the committee has, she said, recommended raising awareness of these possible risks, making sure they are included in the product information. Additional investigations are being launched, Mrs Cooke added.
"If it was me, I would be vaccinated tomorrow," Mrs Cooke added. "But I would want to know that if anything happened to me after vaccination what I should do about it and that's what we're saying today."
Welcoming the review's endorsement of the vaccine as safe and effective, German Health Minister Jens Spahn added, "Doctors should be informed about the risk of venous thrombosis in women under 55 years of age, so that they in turn can inform patients."
"There were a few very unusual and troubling cases which justify this pause and the analysis," French immunologist Alain Fischer, who heads a government advisory board, told France Inter radio. "It's not lost time."
In Germany, the health ministry also pointed to a small number of rare blood clots in vaccinated people when justifying its decision. It postponed a summit on extending the vaccine rollout ahead of the EMA's announcement.
Other countries, such as Austria, halted the use of certain batches of the drug, while Belgium, Poland and the Czech Republic were among those to say they would continue to administer the AstraZeneca vaccine.
Decisions to halt rollouts of the AstraZeneca vaccine were criticised by some politicians and scientists.
A spokeswoman for Germany's opposition Free Democrats said the decision had set back the country's entire vaccination rollout. German Greens health expert Janosch Dahmen, meanwhile, argued that authorities could have continued using the drug.
Dr Anthony Cox, who researches drug safety at the UK's University of Birmingham, told the BBC it was a "cascade of bad decision-making that's spread across Europe".