Jeremy Hunt has urged the British Medical Association (BMA) to return to the negotiating table instead of carrying on with "unnecessary strikes" after the first walkout by junior doctors in 40 years.
The Health Secretary said the union should hold fresh talks with the Government about "how to improve patient safety" following the breakdown of negotiations over the contract.
He told the BBC: "The right thing to do is to sit round the table and talk to the Government about how we improve patient safety and patient care, not these very unnecessary strikes."
Mr Hunt told BBC Radio 4's World at One that "nearly 40% of junior doctors" had turned up to work.
He said: "This is a wholly unnecessary dispute. We want all NHS patients to have the confidence that they will get the same high-quality care every day of the week.
"At the moment, for example, if you have a stroke at the weekends you are 20% more likely to die. That cannot be right and that's something that every doctor wants to sort out as well."
Setting out his plans for a seven-day service, he added: "We recognise that if doctors are too tired they are not going to be able to give safe care to patients.
"But right now what happens is when a junior doctor is asked to work at weekends - which they do a lot - they go into an A&E department where, for example, there will be half as many consultants working on a Sunday compared to a weekday despite it being one of the busiest days.
"It is a pretty exhausting experience. You wouldn't, as a pilot, like to turn up at Heathrow Airport and be told 'I'm really sorry but as it's a Sunday you don't get a co-pilot, but off you go to New York'.
"The Academy of Medical Royal Colleges says junior doctors feel clinically exposed at weekends and that's what we are trying to sort out."
Mr Hunt said the Government "will go back to Acas any day".
A spokesman for the British Medical Association (BMA) said the figure of almost 40% was unsurprising.
He added: "Since we asked junior doctors who would be covering emergency care to go into work today it is hardly surprising that they have done so along with those who are not members of the BMA.
"The simple fact is that the Government cannot ignore the thousands who have today made it quite clear what they think of the Government's plans."
Mr Hunt said the strike was "very disappointing" and added: "I take responsibility for everything that is happening in the NHS but when we have had eight studies in the last five years - it's not just strokes, the mortality rate for newborns is 7% higher at or around weekends, the mortality rate for emergency surgery is 11% higher. I can't, in all conscience as Health Secretary, sit and ignore those studies."
He added: "We have to do something about this, people get ill every day of the week. All doctors want to have a service where we offer fantastic care.
"This new contract actually reduces the maximum hours doctors can be allowed to work."
He said the Government had offered to put in financial penalties for hospitals which get doctors to work longer hours.
He said the current situation meant doctors were encouraged to work long hours.
"We say if you pay doctors four-times their salary for working unsafe hours you are creating a perverse incentive for doctors to actually work hours that are too long."
Mr Hunt said he was willing to work with the BMA, adding: "I will go back to Acas any day and I think that, in the end, we all have a shared vision in the wake of the tragedy of what happened in Mid Staffs to make the NHS the safest, highest quality, care in the world."
Around 100 picket lines have been put in place across England for the strike, with a large concentration in and around London.
Some junior doctors in the West Midlands have refused to go back to work despite an order from their NHS trust.
Sandwell General Hospital in West Bromwich declared a "level 4" major incident and said its junior doctors must return to the wards to relieve the pressure.
But some doctors have accused the hospital of pre-planning the incident after a letter from the NHS trust's medical director was sent to them on Tuesday morning, but was dated Monday.
The letter from Dr Roger Stedman, medical director at Sandwell and West Birmingham Hospitals NHS Trust, said: "Sandwell General Hospital is now at escalation level 4 and is reporting an internal incident".
It said "all junior doctors providing ward-based care need to attend work", adding: "Over the past few days there has been a surge in activity which has continued today."
Dr Stedman said it would "be unsafe to deliver care to all our in-patients with a reduced workforce."
A spokesman for the BMA said doctors in Sandwell should continue to strike until further notice.
Dr Johann Malawana, chair of the BMA junior doctors' committee, said the move by Sandwell and a letter from NHS medical director Sir Bruce Keogh amounted to bullying.
He said there had been "last minute, inept and heavy-handed attempts to bully junior doctors lawfully taking industrial action back into work".
He added: "We deeply regret the level of disruption caused, but this is a fight for the long term safety of patients and junior doctors' working lives."
In Sandwell, some doctors stood firm on the picket line despite being called back to work.
Bridget Riley, who works in the gastroenterology unit at the hospital, said there was an "internal capacity incident" at the trust, which "means we're under more pressure than normal".
She said there had been several similar incidents in recent weeks due to winter pressures on the NHS.
Ms Riley told Sky News that doctors should only be ordered to work if the incident was "unpredictable", rather than something that was known about on Monday.
She added: "Patient care is at the centre of what we do but this strike has been known about.
"All the consultants have been asked to come in, many who support junior doctors. Elective procedures have been cancelled so really this is no different to Sunday, should you come into hospital on a Sunday."
Mr Hunt said he understood that doctors in Sandwell had actually returned to work.
"As I understand it in the latest update I had on the Sandwell situation, the doctors on the ground ignored the national BMA instructions and did go back to work. I think the trust are in the process of de-escalating those situations.
"I think that shows the value of junior doctors - in the end they do want to the right thing for patients and I salute them for it."
Junior doctors - the term for doctors working below consultant level - represent a third of the medical workforce and just over 37,000 of more than 50,000 junior doctors are members of the BMA.
Despite last-ditch talks to prevent the strike, around 4,000 operations and procedures have been cancelled, with thousands more routine appointments also postponed.
The basis for the current round of negotiations is the Government's offer from early November, including an 11% rise in basic pay for junior doctors.
This is offset by plans to cut the number of hours on a weekend for which junior doctors can claim extra pay for unsocial hours.