Emergency department presentations for flu have increased as staff continue to fall victim to the viruses.
About 2000 workers are absent from hospitals on an average day.
After two years with few cases, Health Minister Brad Hazzard says a "horror flu season" has "hit NSW earlier and harder than it has for many years".
"It is absolutely crucial that you go and get your flu vaccine as soon as possible," he said.
There have been 14,812 reported flu cases and 3349 have attended emergency departments with influenza-like illnesses in NSW this year, a third of them in the past week.
More than 8000 cases of COVID were reported on Tuesday, with 1234 people in hospital with the virus, 38 of them in ICU.
The flu brought more than 1100 people to emergency departments last week, with 150 admitted to hospital and six admitted to critical care units.
Health Secretary Susan Pearce said the double whammy of a flu resurgence in an unrelenting COVID-19 pandemic put emergency departments "under significant pressure".
It also comes as the health system tries to get on top of a backlog in elective surgeries.
"Please do not call triple zero or attend emergency departments for non-urgent issues," she said.
"We are urging the community to support us during this challenging period by making sure those who need emergency medical care can receive it by saving ambulances and emergency departments for saving lives," she said.
Anyone unsure whether they should go to hospital should visit healthdirect.gov.au or call Healthdirect on 1800 022 222.
Chief pediatrician Matt O'Meara said children aged six months to five years were particularly vulnerable to flu, with at least 10 per cent of youngsters in hospital with the virus so sick they needed intensive care.
Of the 165 children under five years old that presented to hospitals with a flu like illness last week, 27 were admitted.
"Parents can reduce the risk of that happening just by getting their child vaccinated," Dr O'Meara said.
About 11 per cent of children under five in NSW have been vaccinated and about 51 per cent of people aged 65 and over.
Both groups are eligible for free vaccines, as are Aboriginal and Torres Strait Islanders of any age over six months, as well as people who have serious medical conditions or are pregnant.
NSW Health public health pathology director Dominic Dwyer told AAP it was important to reduce any barrier to obtaining a vaccine in order to increase uptake.
"That can be things like availability of a vaccine, locations where you can get vaccinations, the cost of vaccinations, all of those sorts of things," Professor Dwyer said.
Queensland announced on Monday it would provide free vaccines for all for a month.
"That's an example of strategies you can take to try and increase vaccination rates ... you need a combination of approaches to get people vaccinated," Prof Dwyer said.
NSW is also looking at providing free vaccines, and the government was working with pharmacists and GPs on a strategy.
"Hopefully we will be able to follow a similar path (to Queensland) but it's a little too early yet," Mr Hazzard said.
"We've just got to make sure the system work across the board."
As well as vaccines, the simple precautionary habits people picked up during the pandemic such as mask wearing, handwashing, and staying at home when you're sick could all help reduce flu transmission, Chief Health Officer Kerry Chant said.
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