The number of coronavirus cases in Australia has reached 565, including six deaths.
Professor Kelly said the vast majority were people who had travelled overseas with 100 cases locally acquired.
Australia had a top quality system to monitor medicine shortages, he said.
All suppliers must tell health authorities if there is a shortage on the horizon.
"We have not had that from any suppliers," Professor Kelly said.
In addition, some prescription medicines will be limited to one month's supply.
Pharmacists will be strongly encouraged to limit dispensing and sales of all other medicines.
Professor Kelly said he recognised people were anxious, but panic buying of medicines needed to stop.
NSW chief medical officer Kelly Chant said there was misinformation on social media suggesting paracetamol could cure coronavirus.
"Panadol does not treat COVID-19, but (treats) the symptoms which might be fever, muscle aches and pains," she told reporters in Sydney.
The number of coronavirus cases in NSW has jumped above 300, with close to 50 cases believed to be locally transmitted.
Meanwhile, authorities across state government agencies have decamped to the Rural Fire Service NSW headquarters in order to liaise more effectively and quickly.
NSW chief health officer Dr Kerry Chant told reporters on Thursday there were 307 confirmed cases of COVID-19 in the state, up from 267 on Wednesday.
Of this number, almost 130 were acquired overseas, including recent returnees from virus-hit areas in Europe, the UK and the US.
Some 70 cases remain under investigation.
Dr Chant said the initial precautionary approach of hospitalising all confirmed COVID-19 cases had been abandoned as cases rise.
"It's reassuring that many of our cases continue to be mild with currently six patients in intensive care units. Many of our patients are being managed in the community and being managed at home and we are only admitting patients now that require hospital care," Dr Chant said.
"We are following up and we are working in a whole-of-government way to ensure that people are doing the right thing."
Premier Gladys Berejiklian thanked NSW residents for adhering to new social distancing regulations, alongside the limitation of outdoor gatherings to fewer than 500 people and indoor to fewer than 100.
She said she'd brought a number of agencies into the RFS headquarters - including police, health, transport and education - in order to integrate responses to COVID-19.
"What you see here is the complete integration of police, health, education, transport, and many other government agencies working together to provide safety to our citizens, but also important information in a timely way," Ms Berejiklian told reporters on Thursday.
"All of our experts in this room are coordinating a whole-of-government response [and] will have that data information at their fingertips."
NSW Health on Wednesday said an 86-year-old man previously confirmed to have COVID-19 died on Tuesday night in a Sydney hospital, taking the state's toll to five.
NSW schools will remain open but there'll be no assemblies, with strict bans on sick students and teachers. Regular hand washing will be enforced.
Ms Berejiklian says there's "no rationale" for closing schools, with health experts advising they should remain open.
Splendour in the Grass, Groovin the Moo and the Sydney Film Festival are among events cancelled or postponed this week.
Universities are suspending face-to-face classes and businesses are urging staff to avoid the office. A number of church and mosque services have also been suspended.
NSW Police, meanwhile, is halting major roadside drug and alcohol testing operations over hygiene concerns.
As of Tuesday afternoon, only people who have recently travelled from overseas or have been in contact with a confirmed COVID-19 case and experienced symptoms within 14 days are advised to be tested.
If you believe you may have contracted the virus, call your doctor, don’t visit, or contact the national Coronavirus Health Information Hotline on 1800 020 080.
If you are struggling to breathe or experiencing a medical emergency, call 000.