The first minister added: "I am not standing here saying, and we have not said at any stage, that some patients are not waiting longer during these winter times than we would want them to wait".
"All patients attending the emergency department are assessed and those with more urgent or serious health issues continue to be given priority".
"Over the last month we have seen office staff having to volunteer to help Global Positioning System and hospital staff to cope with the demand". No other trust was below 57 per cent.
Meanwhile trusts up and down the country are seeing no let up in pressure in the new year, with some fearing the worst is yet to come.
The Scottish Conservatives called for a moratorium to be introduced to halt the decline in hospital beds.
Plus, 1.7% of the patients waiting for one of the 15 key diagnostic tests at the end of November 2017 had been waiting six weeks or longer from referral, compared to the 1% operational standard.
"In particular, it was an extremely challenging and demanding New Year weekend, with huge pressure in our A&E department and on our bed capacity".
"However, we are of course sorry for any extended waiting times experienced by patients and their families during this exceptionally busy period".
"We'd like to thank the public for their patience during this hard time and to our staff who have been going above and beyond coping in extreme circumstances".
48 people have died from flu this winter in the United Kingdom after the virus killed 24 people in the last week of 2017, figures released by Public Health England show.More news: Ellen DeGeneres Reveals That Her Father Passed Away
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A hospital spokesman said: "We would like to extend our honest apologies to Esme Thomas and her family, and to all our patients who have had to spend much longer in A&E than normal waiting for a hospital bed".
Dr Liz Mearns, medical director from NHS England's regional office, said: 'It's important we protect young children from the flu virus and get them vaccinated now.
Finally, reporting that 120 patients a day are being managed in corridors, with some dying prematurely, an average of 10-12 hours from decision to admit a patient until they are transferred to a ward and patients sleeping in clinics as makeshift wards.
Staff have been faced with rising numbers of flu cases and respiratory illness, with 48 flu-related deaths in England so far this winter.
Mrs May said flu was putting extra pressure on services and encouraged people to act on the advice the NHS is giving.
The Scottish Ambulance Service reported an nearly 40 per cent increase in the number of calls on Hogmanay alone while NHS 24 received more than 45,000 calls in the four days over Christmas.
PATIENTS are dying in hospital corridors as waiting time targets in A&E departments hit their lowest levels in 14 years, Theresa May has been warned.
The Royal College of Surgeons said it was "disappointing" that just 77.3% of patients at major A&E departments were treated within four hours, worse than in December 2016 when 79.3% of patients were seen.
We remain hopeful and committed to improving the care of patients in Emergency Departments throughout the UK.