Sandwell Hospital in West Bromwich has said it needs all of its trainee doctors to abandon industrial action immediately because "a very high number of patients have been admitted over the past two days".
The medical director of the hospital's NHS trust, Dr Roger Stedman, told striking staff it "would be unsafe to deliver care for all our in-patients with a reduced workforce".
However, the British Medical Association has told affected medics to continue striking until NHS England has confirmed - and the BMA has agreed - "that a major unpredictable incident is taking place".
About 38,000 junior doctors walked out for 24 hours from 8am on Tuesday following a bitter dispute over pay and conditions, which the BMA claims has left trust in the Government at "an all-time low".
But Downing Street is urging the BMA to return to negotiations, with David Cameron's spokeswoman claiming that 15 out of 16 demands made by junior doctors had been met.
She claimed a full seven-day-a-week health service was needed because mortality rates among stroke victims were 20% higher at weekends, while newborn deaths were 7% likelier on Saturdays and Sundays.
Junior doctors continuing to strike outside Sandwell Hospital told Sky News there had been several "level four" incidents in recent weeks - but claimed they hadn't been called at home and ordered to work on those occasions.
It follows accusations that the head of NHS England, Sir Bruce Keogh, has attempted to thwart lawful industrial action by lowering the thresholds under which hospitals can call junior doctors back into work under any circumstances.
Contingency plans had already been put in place for junior doctors to resume duties in the event of "a transport or security incident with many casualties that had overwhelmed a hospital".
But the BMA claims medics could be at risk of disciplinary action from the General Medical Council if they refused to cross the picket line for "routine circumstances which can occur almost daily".
In the run-up to the walkout, the union had warned striking members that some hospitals may try to "move" the goalposts by declaring an emergency and forcing doctors off picket lines.
Anne Rainsberry, national incident director for NHS England, said Sandwell Hospital reported "it has been experiencing exceptional and sustained pressure" - leading to the "level four" escalation.
Both sides in the row have stressed that urgent care across England will not be affected by the strike, but patients are being urged to only attend A&E wards if they have a genuine emergency.
But Katherine Murphy, chief executive of the Patients Association, has warned the strike will still cause "a great deal of distress for many patients".
She added: "At a time when hospitals are struggling to cope with patient demand, the cancellation of operations and appointments will increase pressures across NHS services that are already stretched to breaking point."
Junior doctors are striking over a proposed contract which reduces the hours in the evenings and at weekends that qualify for pay premiums, but increases basic pay instead.
The Government says the contract will help hospitals to provide more seven-day services for patients.
However, doctors believe it will cut their pay in the long term and remove safeguards that prevent them from working excessive hours.
Yesterday, the Prime Minister branded the walkout as "not necessary and damaging", warning: "You can't have a strike on this scale in our NHS without there being some real difficulties for patients and potentially worse."
But Nadia Masood, who has been a junior doctor for 11 years, retorted: "I, and all the doctors that are striking, genuinely believe that this contract is more unsafe than this strike could ever have the potential to be."
This is the first of three strikes planned by the BMA.
On 26 January, affected doctors will only provide emergency cover for 48 hours from 8am. This will be followed by the first-ever full walkout between 8am and 5pm on 10 February.
"Both sides must remember that their first concern must always be patients, who deserve much better than this," the Patients Association said.
