Health Secretary Jeremy Hunt has apologised to patients in England who have had their operations postponed.
Non-urgent treatments had already been cancelled until mid-January, but NHS England said on Tuesday that would now be extended to the end of the month.
It came after hospitals reported they were struggling to cope with the surge in patients being seen since Christmas.
At least 17 hospital trusts - one in 10 - have declared a major incident in the last 24 hours, the BBC understands.
Bosses said they had been forced into the move as patients were experiencing long waits in A&E and being left on trolleys in corridors because there were no beds available.
Some ambulance services have even started asking 999 callers with less serious problems to make their own way to hospital so they can prioritise the most life-threatening calls.
Of the decision to cancel operations, Mr Hunt said it was "absolutely not what I want".
But he said the move was needed given the pressure hospitals were under.
"This is the busiest week of the year for the NHS."
And he also said the whole country was grateful for the work NHS staff were putting in working "incredibly long hours through the night, beyond the call of duty in every possible way".
His thanks were echoed by Prime Minister Theresa May, who also denied the health service was in crisis.
"The NHS has been better prepared for this winter than ever before," she added.
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Problems have also been reported in other parts of the UK.
The Welsh government said the health service was facing "significant pressure".
Meanwhile, in Scotland there has been a 20% jump in A&E attendances compared with the previous year, prompting an increase in patients waiting more than four hours, and in Northern Ireland the Antrim Area Hospital has been forced to bring in St John ambulance volunteers to help with a surge in demand.
NHS England's Prof Keith Willett admitted the pressures were severe - the worst he had seen since the 1990s - but said plans were in place.
As well as the cancelling of non-urgent treatments, such as knee and hip replacements, hospitals have been given the green light to put patients on mixed sex wards and to bring GPs into A&E to help deal with patients.
"A crisis is when you haven't got in place mitigations and you haven't got a plan to deal with it," Prof Willett said.
"We've gone into this winter in a way we've never prepared before."
Doctor warns of 'huge tragedy'
But Prof Suzanne Mason, of the Royal College of Emergency Medicine, said the measures were "too little too late" as hospitals simply had no beds free and these treatments would have had to be cancelled anyway.
She added: "Patient safety is being compromised - there's no doubt about that. When patients are in crowded emergency departments and staff cannot actually move between patients and provide the basic level of care that's required, then safety is compromised.
"Patients who spend many hours on a trolley - and these are often elderly patients - they are the sickest patients in our department.
"They are much more likely to have a poorer outcome and even die as a result of their experience in the emergency department. And that is a huge tragedy for us in our specialty and that's why we are so desperate to see things improve."
Reports have emerged of serious problems in a number of places over the past 24 hours:
- Nottingham's Queen's Medical Centre has asked patients to avoid its A&E after being deluged on Tuesday evening
- Southend Hospital said it was dealing with an "internal critical incident" with all its beds full, which has led them to call in extra staff
- A consultant at University Hospitals of North Midlands NHS Trust apologised for "third world conditions" in his hospital department
- Milton Keynes University Hospital is telling people only to attend for emergency treatment
- Two ambulance trusts in the east and north-east of England are on the highest alert
- A concentration of major incidents declared at hospitals across the West Country and south-east
Doctors and nurses have also been speaking about the problems.
Dr Adrian Harrop, an A&E doctor at Scarborough Hospital, said he felt he was "fighting a losing battle" as he was not able to do his job properly and care for his patients in the way he wanted.
Mark Nevison, a senior nurse in the north-east, tweeted he had worked in A&E for 10 years and had "never been so ashamed of the sub-standard care" now being offered.
Meanwhile, patients have been talking about their experiences.
Esther Herbert accompanied her 87-year-old mother to Worcestershire Royal Hospital before Christmas.
"The doors opened and it was just a sea of people," she said.
"There were people on beds all the way down the corridor, as far as you could see."
Labour shadow health secretary Jonathan Ashworth has blamed the pressures on "Tory underfunding".
The health service is in the middle of its toughest cash settlement since it was created.
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