Professor Sir Munir Pirmohamed, chairman of the Commission on Human Medicines, says pregnant women should speak to a healthcare professional before getting the AstraZeneca jab.
He added that people with a history of blood disorders should only have the vaccine if the benefits outweigh the risks.
The advice is being given after 79 people in the UK had blood clots following their first Oxford-AstraZeneca jab up to the 31 March.
Of those people, 19 have died - three under the age of 30.
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