"I wrote to the prime minister saying 'please can you support us in that way' and he very gladly accepted."
The announcement came as NSW recorded its first death from coronavirus since August 16.
The fatality, a man in his 70s, died at Royal North Shore Hospital on Saturday, Ms Berejiklian said, bringing the state's death toll to 55.
There were just two new COVID-19 cases on Sunday, one in hotel quarantine.
The other is a taxi-driver who tested positive on Saturday and NSW Health says anyone who entered his vehicle between September 8 and 18 should monitor for symptoms.
His taxi trips during that time spanned the suburbs of Moorebank, Bankstown, Chipping Norton, Liverpool, Lidcombe, Warwick Farm and Milperra.
Early investigations indicate the driver likely contracted the virus at Liverpool Hospital. He had the COVIDSafe app which is being used to identify contacts.
NSW Health is also working with the driver and 13CABS to identify passengers.
The cab driver stopped at several places for food during this period, meaning all people in those locations are considered close contacts.
The locations include Campbelltown Golf Club in Glen Alpine on September 16 between 2pm and 4.30pm in the TAB area, and Milton Ulladulla Ex Servos Club on September 12 from 2 to 6.15pm.
He also visited Carlo's Italian Ristorante Bar and Seafood in Ulladulla on September 12 from 8pm to 9.30pm, and Bannisters Pavilion Rooftop Bar and Grill in Mollymook on September 13 from 12.30pm to 2.15pm.
Casual contacts are considered to be those who attended Picnic Point Bowling Club on September 18 from 3pm to 6pm, and Campbelltown Gold Club in Glen Alpine on September 16 from 9.30am to 2pm.
NSW Health said taxi passengers should sit in the back seat and wear a mask.
It comes as NSW prepares to accept an additional 500 returned travellers each week into its hotel quarantine system.
The increase will start from September 27 and will take the state's intake to about 3000 a week.
People in Australia must stay at least 1.5 metres away from others. Check your state’s restrictions on gathering limits.
If you are experiencing cold or flu symptoms, stay home and arrange a test by calling your doctor or contact the Coronavirus Health Information Hotline on 1800 020 080. News and information is available in 63 languages at https://sbs.com.au/coronavirus