Care minister Helen Whately said European Commission president Ursula von der Leyen should stick to a commitment not to block pharmaceutical companies from meeting the terms of contracts to supply vaccines.
Ms von der Leyen, who is under pressure over the EU’s relatively poor vaccine rollout, has ramped up the rhetoric this weekend, saying the EU has the power to “forbid” exports, adding: “That is the message to AstraZeneca.”
The warning reflects growing frustration on the continent that the EU is not getting the supplies it expected from the British-Swedish manufacturer.
The Prime Minister is expected to contact his EU counterparts ahead of virtual summit on Thursday where European leaders are due to consider the matter.
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 Government source added.
Reports have suggested the latest focus of the row is on AstraZeneca vaccines produced in the Halix plant in the Netherlands, with officials arguing they should be kept for the EU rather than allowed to be exported to the UK.
Ms Whately told BBC Radio 4’s Today: “What we’re hearing at the moment is some speculation, some conjecture, an element of rhetoric.
“But what is actually important is that the EU and no country should follow vaccine nationalism or vaccine protectionism.
“We expect the European Union to stick by their commitments and I’m sure the Prime Minister will be in contact with European counterparts – he speaks to European counterparts regularly – but I don’t think this debate is helpful to anybody.
“What matters is for all countries to be getting on and deploying and vaccinating their population.”
Asked whether the UK would retaliate if the EU did impose a block on vaccine exports, Ms Whately said: “I don’t think it is very helpful to speculate at the moment. I don’t think this is a helpful line to go down.”
Labour leader Sir Keir Starmer told LBC Radio: “I don’t think the EU is helping itself here, I don’t think it has helped itself much in the last few weeks and months on the whole question of the vaccine.
“I don’t think they should go down this road of banning exports.”
The UK is already facing a squeeze on vaccine supplies in April and Sir Keir said the dispute with the EU needed to be resolved as quickly as possible “because we don’t want any shortage in vaccines to interrupt the rollout in this country”.
The use of the Oxford/AstraZeneca jab in Europe has been hit by fears over blood clots, although the European Medicines Agency concluded it was a “safe and effective” jab.
On Monday, data from a US-led trial showed the vaccine is 79% effective at preventing Covid-19 and offers 100% protection against severe disease,.