A spokesperson for EU Commission president Ursula von der Leyen insisted the bloc just wanted pharmaceutical firms to meet their contractual obligations to the member states on the delivery of Covid vaccines.
Amid a growing row with pharmaceutical giant AstraZeneca, Ms von der Leyen at the weekend said the EU had the power to “forbid” exports, adding: "That is the message to AstraZeneca."
Boris Johnson is now expected to ask European leaders this week to dismiss any proposals of such a block on exports to the UK.
The EU's vaccination campaign is lagging behind the UK's, with the bloc claiming AstraZeneca has "underproduced and underdelivered" on its contract.
Chief spokesperson Eric Mamer told reporters in Brussels on Monday: "The president has given our view of what the situation is and what are the objectives that we are following.
"This is not about banning vaccine exports, this is about making sure that companies deliver on their commitments to the member states and the European Union that are inscribed in the contracts that they have with us.
"Therefore, this is our objective, to make sure that the contracts that we have signed are respected.
"In that context, the president has said that, of course, we see that, actually, companies that manufacture doses in the EU have been exporting very widely – which is in itself a good thing – but that we want to see reciprocity and proportionality in these exports."
Calling Peston: Is the vaccine rollout still on track?
Government sources said Mr Johnson spoke to Ms von der Leyen, along with Dutch and Belgian prime ministers Mark Rutte and Alexander De Croo last week.
He may speak to other EU leaders over the coming days, the source added.
It comes as the UK celebrated “a record-breaking day for the vaccine rollout” in the UK after 844,285 jabs were given to members of public on Saturday.
On Monday, health minister Helen Whately MP said the EU should "keep to the commitment" it made to the UK on vaccines.
"The European Union has made a commitment. Ursula von der Leyen committed to the Prime Minister that the EU would not block countries from fulfilling their contractual obligations to the UK," she told ITV News.
"It's crucial that the EU stands by that commitment," Ms Whately added.
"That commitment is the right thing for them to say, the right thing for them to do, and any alternative to that simply can't be a good thing for anybody.
"The right course of action is for every company to fulfil its contractual obligations, and for countries to support them in doing so.
"It would be fundamentally unhelpful for any country to try and stop parts of production that are happening in their country - these are complex global supply chains."
Ms Whately added: "A better conversation to be having would be one about how we can cooperate and collaborate so we can better maximise the production of the vaccine.
"That has to be a better way forward to protect not only ourselves and those in the EU, but across the world."
Ms Whately told ITV's Good Morning Britain that she had not seen analysis that an EU ban on vaccine exports could delay the UK vaccine programme by two months, but stressed the country is "absolutely on track" in its rollout.
Asked about the Guardian report, the health minister said: "I haven’t seen that but as I’ve said, we’ve been doing a tremendous job with our deployment. We are absolutely on track."
The Prime Minister’s official spokesman told reporters on Monday: “We expect the EU to continue to stand by its commitment.
“Ursula von der Leyen confirmed earlier this year the focus of their mechanism was on transparency and wasn’t intended to restrict exports by companies where they are fulfilling contractual responsibilities.
“We expect the EU to continue to stand by that commitment and it’s important that the whole world works together.
“I would also point to the fact that vaccines are manufactured in many different countries, you are aware the AstraZeneca manufacturers have plants in a number of countries, and, as I say, it’s an international effort.”
The row comes as Boris Johnson prepares to ask MPs to extend coronavirus restriction measures for a further six months.
Ministers say the extension would ensure furlough can continue to apply even after all measures have possibly been scrapped.
Ms Whately told BBC Breakfast: "The road map is on track and indeed we want to lift those restrictions by June 21.
"We have said we will take steps cautiously and we will be driven by the data rather than those dates.
"There are also a number of things which will need to continue and will be continued for a longer period of time.
"So, for instance, the furlough scheme, which the Chancellor extended through to October, and this Act is needed in order to have the furlough scheme.
"Also the sick pay, which means you can get sick pay from day one and, for instance, if you’re isolating from Covid, so there are things we need to have in place beyond the dates in the road map."