Doctors are being urged to return to the negotiating table by Jeremy Hunt, who has described their strike as "wholly unnecessary" and "very disappointing".
Thousands of junior doctors are taking part in the strike across England in a row over a new contract and weekend pay.
The Health Secretary said "nearly 40% of junior doctors" had turned up to work, although it later emerged the figure included those working in urgent and emergency care, who have been asked not to strike by the British Medical Association (BMA).
Mr Hunt said the union should hold fresh talks with the Government about "how to improve patient safety".
He said: "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.
"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."
A spokesman for the BMA said the figure of almost 40% working 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."
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 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.
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 added: "All junior doctors providing ward-based care need to attend work", saying it would "be unsafe to deliver care to all our in-patients with a reduced workforce".
Bridget Riley, who refused to return to work at the hospital, 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."
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 "last minute, inept and heavy-handed attempts to bully junior doctors".
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."
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 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.
NHS England said 39% of junior doctors out of a possible 26,000 had reported for work (including urgent and emergency care doctors). The 26,000 figure is the number of junior doctors who would be expected to be in work on a typical day.
Anne Rainsberry, national incident director for NHS England, said: "It's a tough day, but the NHS is pulling out all the stops, with senior doctors and nurses often stepping in to provide cover."
Tuesday's strike will finish at 8am on Wednesday.
This will be followed by further strikes. There will be a 48-hour stoppage and the provision of emergency care only from 8am on January 26.
On February 10, there will be a full withdrawal of labour from 8am to 5pm.