But this has sparked a row as the BMA has suggested the requests are “politically motivated”.
Ms Atkins promised to start talks with the BMA “in 20 minutes” if the strikes were called off.
Speaking on a visit to London Ambulance Service, she told the PA news agency: “I’ve said throughout this that, please, to the junior doctors’ committee, the moment you call off the strikes, I’ll get back around the table with you within 20 minutes.”
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She said the strikes have to be called off for negotiations to happen, “because the NHS belongs to us all”.
“It doesn’t just belong to the junior doctors’ committee, and for the 1.3 million people who work in the NHS, as well of course for the tens of millions of people it looks after, the NHS cannot be switched on and off on whim.”
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2:47
The longest strike in NHS history
However, the BMA hit back calling it a “political choice” for Downing Street to “stick rigidly to its dogma of not negotiating while strikes are planned”.
Professor Philip Banfield, BMA council chairman, said: “In the past, the government waived this principle for the barrister strikes, so there is no reason for them to waste time and money by refusing to talk now.
“We are clear: we are ready to talk 24/7. Get back around the table, give us a credible offer and we can end these strikes right now.”
The government gave junior doctors an 8.8% pay rise last summer, with an extra 3% offered during the last round of negotiations towards the end of the year.
But the BMA rejected the 3% offer, saying it does not make up for a real-term pay cut of nearly a quarter for junior doctors since 2008.
They want full pay “restoration” to reverse real-term cuts in pay since 2008-9, a new pay mechanism to prevent any future pay decreases against inflation and the cost of living, and a reformed pay review body to “safeguard recruitment and retention of junior doctors”.
More than 20 derogation requests have been submitted to the BMA for this round of strikes, but so far none have been approved.
The union said that NHS England and some trusts are refusing to provide evidence that they have undertaken steps to show they have “exhausted” all other sources of staffing before recalling medics from the picket line.
In a letter to NHS bosses, the BMA accused health leaders of misusing the system and bowing to political pressure to undermine the strike.
NHS England said they will “continue to engage with the BMA in good faith” and they will address the process for considering patient safety mitigations.
Ms Atkins, echoing Mr Sunak’s comments earlier on Thursday, said she backed NHS leaders in making the mitigation requests but this is being done “completely independent of government”.
She said the strikes are having “very serious consequences”, with 88,000 appointments cancelled during the last set in December.
Health officials have warned that this strike will be worse because it coincides with one of the busiest weeks of the calendar year, due to a rising tide of winter bugs and people storing up problems over the Christmas break.
On the first day of the strike on Tuesday, critical incidents were declared at Queen Alexandra Hospital in Portsmouth and by the NHS in Nottingham.
Meanwhile more than a dozen hospitals said that emergency services were busy, with some reporting “extreme heightened pressure”.
Chancellor Rachel Reeves has criticised post-financial crash regulation, saying it has “gone too far” – setting a course for cutting red tape in her first speech to Britain’s most important gathering of financiers and business leaders.
Increased rules on lenders that followed the 2008 crisis have had “unintended consequences”, Ms Reeves will say in her Mansion House address to industry and the City of London’s lord mayor.
“The UK has been regulating for risk, but not regulating for growth,” she will say.
It cannot be taken for granted that the UK will remain a global financial centre, she is expected to add.
It’s anticipated Ms Reeves will on Thursday announce “growth-focused remits” for financial regulators and next year publish the first strategy for financial services growth and competitiveness.
Bank governor to point out ‘consequences’ of Brexit
Also at the Mansion House dinner the governor of the Bank of EnglandAndrew Bailey will say the UK economy is bigger than we think because we’re not measuring it properly.
A new measure to be used by the Office for National Statistics (ONS) – which will include the value of data – will probably be “worth a per cent or two on GDP”. GDP is a key way of tracking economic growth and counts the value of everything produced.
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Brexit has reduced the level of goods coming into the UK, Mr Bailey will also say, and the government must be alert to and welcome opportunities to rebuild relations.
Mr Bailey will caveat he takes no position on “Brexit per se” but does have to point out its consequences.
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Bailey: Inflation expected to rise
In what appears to be a reference to the debate around UK immigration policy, Mr Bailey will also say the UK’s ageing population means there are fewer workers, which should be included in the discussion.
The greying labour force “makes the productivity and investment issue all the more important”.
“I will also say this: when we think about broad policy on labour supply, the economic arguments must feature in the debate,” he’s due to add.
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The exact numbers of people at work are unknown in part due to fewer people answering the phone when the ONS call.
Mr Bailey described this as “a substantial problem”.
He will say: “I do struggle to explain when my fellow [central bank] governors ask me why the British are particularly bad at this. The Bank, alongside other users, including the Treasury, continue to engage with the ONS on efforts to tackle these problems and improve the quality of UK labour market data.”
The proposed legislation would allow the State of Pennsylvania’s Treasurer to invest up to 10% of its funds in Bitcoin, suggesting a multibillion-dollar investment.