The Health Secretary was confronted by a junior doctor live on TV about not resolving the ongoing pay dispute
Steve Barclay was told the pay offer he had made was not "fair or reasonable" as it would fail to address the massive real terms pay cuts staff have faced in the last 15 years.
The British Medical Association's junior doctors' committee co-chair Vivek Trivedi challenged the Tory minister after he suggested doctors were being unreasonable.
Junior doctors will strike for at least three days every month over the summer after pay talks with ministers broke down.
The BMA has said the government's offer of 5% is not "credible", with their next walkout planned for 72 hours from 7am on June 14.
Mr Barclay, who was asked if he was going to budge on a pay offer to end strikes, said: "We have had a number of weeks of negotiations with the junior doctors.
"What is striking is their refusal to move from their demand for a 35% pay rise and in fact in the course of the negotiations, it increased to 49% if you include 24/25."
Speaking on the BBC's Sunday With Laura Kuenssberg programme, he said junior doctors have rejected the offer ministers have put on the table - which is "in line with the offer that the NHS staff council has received" - and have refused to move from demanding a 35% pay rise.
Ms Kuenssberg then invited Mr Trivedi to respond, saying: "The Health Secretary says the ball's in your court and you're being unreasonable?"
The junior doctors' representative said: "I would say a 5% pay uplift this year would still amount to a massive real terms pay cut and would only further the pay erosion that doctors have had to face over the last 15 years.
"And so an offer which does not reverse that trajectory would not be fair or reasonable given that we've seen time and time again what impact erosion has on pay - the erosion of pay has on doctors' morale and retention. Ultimately, it's driving doctors away so we need to do something to prevent this."
Mr Barclay continued: "They haven't moved from 35% - that's the key. There needs to be movement on all sides. We have moved, as a government, from where we were with the pay review body recommendations to the offer we made.
"That offer is part of a wider discussion. There's a range of other things that the BMA have tabled alongside pay that they wish to discuss and we're ready to engage with them. But the key point is that the BMA junior doctors' committee refused to move from their demand for 35% pay rise."
Ms Kuenssberg pressed the Health Secretary on other aspects involved in the dispute including working conditions and staff shortages.
Mr Barclay refused to give a deadline for the publication of the long-awaited NHS workforce plan but insisted it would be published "shortly".
Asked whether the plan would be published next month, he said: "The Government said it is committed to a long-term workforce plan... in the autumn statement the Chancellor set out the commitment to bring forward the long-term workforce plan.
"We've said that we will do that shortly."
The plan was first promised in November 2018.
The interview also saw Mr Barclay admit some of the facilities included in the government's commitment to provide 40 "new" hospitals by 2030 will be refurbished sites rather than built from scratch.
Pressed on the suggestion that all 40 will be "brand new", Mr Barclay acknowledged the pledge covers a range of building work.
He said: "Some of the schemes include, for example, a hospital being gutted and fully refurbished - if you look at Charing Cross for example, that's exactly what we'll be doing.
"And we'll be starting work to decant some of the facilities and then refurbish, so there's a range of things".
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