Theresa May has said the NHS had never been better prepared for winter than it was this year, despite 16,900 people having to wait more than 30 minutes to be seen by staff at emergency departments over the Christmas week.
Thousand of operations have been delayed for up to a month to help cope with the crisis.
The prime minister told the BBC's The Andrew Marr show the postponement of operations was "part of the plan".
"The NHS has actually been better prepared for this winter pressures than it has been before.
"It's about making sure that those who most urgently need care are able to get that treatment when they need it," she said.
Mrs May praised the "fantastic job" NHS staff were doing.
"They have been working really hard over this time of winter pressure and really delivering for people," she said.
Last week, an elderly woman who called 999 complaining of chest pains died while waiting almost four hours for her ambulance to arrive.
In a separate case another pensioner died following a seven-hour wait for a hospital bed.
Andrew Marr raised the case of Leah Butler-Smith, whose mother was forced to wait five hours, including an hour outside A&E in an ambulance, before being seen by a doctor at Broomfield Hospital in Essex after suffering a stroke.
Marr told Mrs May if he had had to wait five hours when he had his stroke, he "would not be here talking to you".
In response, Mrs May said: "I recognise that people have concerns if they've had experiences of that sort.
"But if we look at what is happening across the NHS, what we see is that actually the NHS is delivery for more people, it is treating more people and more people are being seeing within the four hours every day than has been a few years ago."
She conceded that there was "more to do".
"Of course we want to ensure that those operations can be reinstated as soon as possible, but it's about making sure that those who most urgently need care are able to get that treatment when they need it," she said.
Mrs May said the government had put extra funding into the social care system.
"We have worked with hospitals and with local authorities to identify how we can reduce those delayed discharges, ie patients being kept in hospital when they shouldn't be."
Dr Chaand Nagpaul, chairman of the British Medical Association Council, said: "The Prime Minister appears to be in denial about the scale of the pressure facing the NHS."
He added it is "astonishing" that Mrs May claims the NHS was prepared for this winter and also suggested an "honest debate" is needed about the required investment and support.
The prime minister confirmed she would be staying in the job for "as long as people want me to serve" as she prepares to re-shuffle her cabinet team.
"I'm not a quitter. I'm in this for the long term," she said.