It comes after the Herald reported this week that nurses at nearby Middlemore Hospital were also struggling with severe staff shortages and a surge in ED presentations as the hospital tried to fill 208 fulltime nursing vacancies.
In the letter, Claire said Auckland Hospital hit a new record on Tuesday with the highest ever occupancy.
At 7am that day there were 825 adult health inpatients. That was compared to an average of 730 to 750 inpatients at one time during the winter months last year.
In the seven days prior to Tuesday, 1450 adult patients presented to Auckland City Hospital's emergency department - compared to 1234 during the same period last year.
"I know that this will also have put added pressure on our support services and community services as well as our emergency departments and wards.
"The hospital was fully flexed with every available bed in use.
"We remain at high occupancy with a number of flex beds still in use.
"There may be more very busy days to come – we are not through winter yet," Claire said in the letter.
Speaking to the Herald last night, Claire said the occupancy figures were unprecedented, but "thanks to our planning and the efforts of our people we were able to safely manage the high numbers of patients".
"The public can be assured that if they or their loved ones need immediate hospital-based attention, we have the plans in place to provide a high standard of care.
"If it's a serious or life-threatening emergency, don't hesitate to go to the emergency department or call 111."
Association of Salaried Medical Specialists executive director Ian Powell said the surge in presentations was largely due to increased demand for public hospitals and more people becoming acutely unwell.
"I don't feel confident that this Government is addressing this issue, particularly when it comes to severe workforce shortages."
Health Minister David Clark said nine years of underfunding wouldn't be fixed right away. But the record $2.8 billion increase in operating funding for DHBs and $1.7b for new and upgraded hospitals in the May Budget shows "we're getting on with the job of putting things right".
"It also underscores the need for the increase in funding across our health care services that this Government has put in place to build capacity and sustainability."
Ministry of Health chief medical officer Dr Andrew Simpson said the ministry was aware of the winter pressure on hospitals and DHBs.
"We know that hospital staff do a vital job in our communities. This week has been a reminder of their importance in dealing with the many illnesses and conditions affecting people along with the additional ailments that winter brings."
General advice to the public:
You can help protect yourself and your whānau from serious illness this winter:
• Visit your pharmacy for minor health conditions and queries.
• See your GP early for all non-urgent health concerns.
• Visit your local accident and medical clinic for minor illnesses and injuries – you can find an appropriate GP or accident and medical clinic by visiting Healthpoint.
If you're unsure where you should go, call Healthline for FREE advice from a nurse on 0800 611 116. Translators are available 24/7.
If it's a serious or life-threatening emergency, don't hesitate to go to the emergency department or call 111.