Boris Johnson is expected to urge EU leaders this week to dismiss any proposals to block coronavirus vaccine exports to the UK.
European Commission President Ursula von der Leyen insisted over the weekend that the EU has the power to "forbid" exports of coronavirus doses, adding: "That is the message to AstraZeneca."
And EU Commissioner Mairead McGuinness refused to rule out a ban, saying that "everything is on the table".
The warnings reflect growing frustration on the continent that the EU is not getting the supplies it expected of the Oxford/AstraZeneca COVID-19 vaccine from the British-Swedish manufacturer.
Many European countries are experiencing a surge in infections amid the slow vaccine rollout, with France and Italy among those forced into new restrictions.
Mr Johnson is expected to contact his EU counterparts ahead of virtual summit on Thursday where European leaders are due to consider the matter, The Financial Times reported.
Government sources said the prime minister 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 government source added.
Speaking on Sky News’s Sophy Ridge On Sunday programme, Defence Secretary Ben Wallace told Sky News that any bid by the EU to block vaccine exports would be "counterproductive" and damage the bloc’s reputation globally.
He said: "If contracts and undertakings get broken, that is a very damaging thing to happen for a trading bloc which prides itself on the rule of law.
"It would be counterproductive because the one thing we know about vaccine production and manufacturing is that it is collaborative.
"If we start to unpick that, if the Commission were to start to do that, I think they would undermine not only their citizens’ chances of having a proper vaccine programme, but also many other countries around the world with the reputational damage to the EU, I think, they would find very hard to change over the short-term."
Meanwhile, Mr Johnson said Saturday was "a record-breaking day for the vaccine rollout, with 873,784 people receiving a jab" in the UK.
Health Secretary Matt Hancock tweeted: "For the second day running, the team has reached a new record number of vaccines administered in a single day – 873,784.
"This mammoth team effort shows the best of Britain – thank you to the British public for coming forward."
NHS chief executive Sir Simon Stevens said: "In just one day we vaccinated the equivalent of the entire adult populations of Liverpool, Southampton and Oxford combined."
But Professor Jeremy Brown, a member of the Joint Committee on Vaccination and Immunisation, said the jab rollout in the UK may be delayed "slightly" due to problems with supplies.
He told Sky News: "It has always been the supply of vaccine that has been the concern that might delay things, and yes, I suspect our vaccine programme will be delayed slightly compared to where we thought it might have been a few weeks ago.
"But then we are ahead of schedule, so we are probably going to fall back to the original schedule and end up with everyone who is an adult being offered a vaccine by towards the middle to end of the summer."
Analysis: Minister hints at retaliation if EU impose vaccine export ban
By Rob Powell, political correspondent
He didn’t say it explicitly, but Ben Wallace is clearly hinting that the UK could retaliate if the EU decided to block vaccine exports.
Any kind of cross-border jab war would not be good for either side because the supply chains are so interdependent.
For example, if the EU blocked shipments of the Pfizer vaccine going to the UK, Westminster may respond by stopping the Yorkshire-made lipids that are needed for the jab going over to Belgium.
But the European Commission is under immense pressure from member states.
A combination of over-caution regarding the Oxford jab and stuttering supplies from AstraZeneca has seen the bloc’s vaccine rollout get off to a sluggish start.
Brussels chief Ursula von der Leyen raised the temperature further by pointedly mentioning that no vaccine stocks had come from the UK recently.
European leaders will meet on Thursday to discuss the way forward.
Set against febrile Brexit situation, a ban on exports to the UK would be an major step, especially given apparent reassurances Boris Johnson extracted from the EU earlier this year.