"The company... has to honour the contract it has with member states," European Commission President Ursula von der Leyen said on Thursday.
She spoke after EU leaders held a summit to discuss vaccine supplies.
Meanwhile, French President Emmanuel Macron told reporters it was "the end of naivety" from the EU.
Vaccine rollouts in EU states have started sluggishly, and the bloc has blamed pharmaceutical companies - primarily AstraZeneca - for not delivering promised doses. AstraZeneca has denied that it is failing to honour its contract.
"I think it is clear that first of all the company has to catch up," Mrs von der Leyen told a news conference after the virtual leaders summit.
"[It] has to honour the contract it has with European member states before it can engage again in exporting vaccines," she said. "We want to explain to our European citizens that they [can] get their fair share."
The EU has been criticised, primarily by the UK and the World Health Organization (WHO), for so-called vaccine nationalism after it introduced export controls on jabs produced within the bloc.
In response, UK Prime Minister Boris Johnson warned that "blockades" were not "sensible".
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