Police say going for a surf at Cronulla is a form of exercise under the new Stay at Home laws, but loitering on the beach or in the car park could result in a fine.
"The [Cronulla] beaches are still open," Sutherland Shire Police Area Command duty officer, Inspector Rick Johnson, told the Leader on Wednesday.
"People can go for a surf, but they still need to adhere to the regulations regarding no more than two people together and keeping the required distance apart.
"You shouldn't be sitting on the beach. When you come out of the water, grab your gear and go home."
Inspector Johnson said police were patrolling beaches and parks and responding to calls that have come in from various parts of the shire about people breaching the laws.
Mayor Carmelo Pesce saw an example of police enforcement at Elouera beach on Tuesday.
"A police car was driving up and down Mitchell Road and I saw it pull up and put on the siren," he said.
"There were people who had come out of the surf and were congregating in the car park, and the police moved them on."
Cr Pesce said there were seven kilometres of beaches stretching from Cronulla to Boat Harbour that could be used by people for exercise, so people should spread out.
"Observe the rules of no more than two people together and keeping 1.5 metres apart," he said.
Cr Pesce said the council was awaiting further Government Gazette details to see whether signs placed at the beaches needed to be revised.
A ministerial directive published in the NSW Government Gazette said anyone who left their home without a "reasonable excuse" could be fined up to $11,000 or jailed for six months.
Reasons for being outside the home include obtaining food or other goods and services, work and education that cannot be done from home, exercise, medical or caring needs and a limited number of other reasons.
Police Commissioner Mick Fuller said on Wednesday police were enforcing the new laws but had yet to issue a fine for breaching social distancing or Stay at Home laws.
"I know there has been some criticism of police, which I don't accept. I accept criticism of my leadership certainly," he said.
"In the last 24 hours only one infringement has been issued in the entire state for a breach of self-isolation and that infringement does not relate to increased powers in place since midnight Monday.
"If people continue to flout the rules and ignore the message, then tickets will be issued.
"We continue to re-educate our force almost daily in terms of changes around powers and policy.
"I have asked police to show a high level of discretion.
"I would ask the community to work with us.
"We understand these changes can be difficult particularly with our culture.
"I know there will always be 'what ifs' that will be challenging, but the message is simply that small numbers are safe and stay home where you can.
"If you need to go to work, please continue to do so. It is important for our economy long term.
"If you need medical assistance, pharmacy, doctor, hospital, you can leave. If you need food you can leave.
"If you are driving home and need a takeaway coffee, there is nothing wrong with jumping out of the car and getting a coffee, just don't sit down and have it there."
In a TV interview, Mr Fuller said, if a mother was sitting in a park with children crawling or running around her, he would regard that as the children exercising.
However, it could be complicated "if everyone went to the park at the same time" and the mother or children unknowingly spread the disease.
Premier Gladys Berejiklian said, "In the main, everyone has responded favourably, and we deeply appreciate it".
"We know its a really frustrating time for our citizens, but we also appreciate we are all doing this to keep each other safe and especially top keep those most vulnerable safe," she said.
