Moving all teachers up the queue for COVID vaccines would risk more overall deaths among more vulnerable groups, cabinet minister Liz Truss has suggested.
The international trade secretary pushed back against Labour's call for all teachers and school staff to be vaccinated during the upcoming February half-term, in a bid to get all children back in classrooms.
Former prime minister Tony Blair became the latest high-profile figure to support the earlier vaccination of teachers, which he suggested could take as little as two days to complete.
And a senior Conservative MP has also said there is a "very compelling case" for teachers to be prioritised.
The government is currently aiming to offer a first dose of a COVID vaccine to 15 million of the most vulnerable by 15 February.
This includes older care home residents and staff, everyone over 70, all frontline NHS and care staff, and those who are clinically extremely vulnerable.
After the first four priority groups are offered a vaccine by the middle of next month, the Joint Committee on Vaccination and Immunisation (JCVI) has recommended vaccines are then offered to the next five priority groups under the first phase of the vaccination programme.
This includes all those aged over 50 and those aged over 16 with underlying health conditions that puts them at higher risk.
Ms Truss suggested - due to a lack of spare vaccine supply - the government would not be adding teachers to the first nine priority groups to receive jabs at this stage of the UK's vaccination programme.
"The issue is that for every person you vaccinate who isn't in the most vulnerable group, that's somebody in the most vulnerable group who isn't getting their vaccine and who is more likely to die in the next few weeks and months," she told Sky News' Sophy Ridge on Sunday programme.
"I just don't think that's right and that is the decision made by the independent committee that we are going to vaccinate first the over-70s and those in the most vulnerable group and then the over-50s.
"It's right that we do have an independent committee that looks at the priorities.
"Of course, we want everybody to be vaccinated, of course we want the schools to be open, but we are facing a really difficult choice and the most important thing is protecting lives and that is why we've had to deal with vaccine priorities in the way we have."
She added: "There isn't spare capacity to vaccinate other people, we do have to prioritise those who are most vulnerable to dying and that is the stark truth we face."
On Friday, more than 480,000 people in the UK received their first dose of a COVID vaccine and Mr Blair suggested - with around 500,000 teachers in the UK - that the prioritisation of teachers would only cause a short delay to the vaccination of other groups.
"If you decided you wanted to vaccinate all the teachers, you could do it in a very short space of time," he told the same programme.
"I know you would delay it somewhat but you probably could get that done in a couple of days and the point is - I know there are arguments on the other side and obviously speaking as somebody who is in that age category, of course I want the vaccine as soon as possible - but I think on the other hand it is so important to get the children back into school."
Conservative former health secretary Jeremy Hunt, now the chair of the House of Commons health committee, said there was a "very compelling case" for prioritising teachers for vaccines.
But he added that for some in the NHS, vaccinating more elderly age groups was a "real priority" in order to ease pressures on hospitals.
"If we can do the teachers, everyone will want to do that but we just need to listen to that scientific advice to make sure we get the balance absolutely right," Mr Hunt said.
Labour's shadow Cabinet Office minister Rachel Reeves said her party were asking the JCVI to consider prioritisation for those workers - such as teachers, bus drivers, taxi drivers, police officers or supermarket workers - who are most exposed to the virus to get access to vaccines "at a bit of an earlier stage".
She denied Labour were asking for the JCVI's current prioritisation advice to be overridden, adding: "We are asking the JCVI to look at the evidence and to see whether with the ramp up of the production and the distribution of the vaccine going so well, whether we can bring more people in at an earlier stage to protect them."
Amanda Milling, the Conservative Party's co-chair, accused Labour of having "abandoned the science" and of "playing politics with the vaccine".