Currently, two adults from the same household, along with their dependent children, can visit another home in NSW under the existing COVID-19 restrictions.
"I want to say to the people of New South Wales, we're at this point in the pandemic because everybody has pulled together and done the right thing. We have to keep our vigilance," Ms Berejiklian told reporters on Sunday morning.
The new relaxing of restrictions announced by the premier will also allow 10 guests at weddings, 20 people at indoor funerals, and 30 at outdoor funerals.
Religious gatherings and places of worship can also welcome up to 10 people.
Ms Berejiklian urged the state to behave responsibly once restrictions are lifted.
"Every time you leave the house, you have to assume you have the virus or somebody you're going no contact with as the virus. That is the only way we will keep this deadly virus at bay," Ms Berejiklian said.
"Just because we're easing restrictions doesn't mean the virus is less deadly or of less threat,".
Outdoor equipments including gyms and playgrounds can be used with caution, with people encouraged to sanitise the equipment, and swimming in outdoor pools will be allowed.
"Please acknowledge and assume that every time you use an outdoor piece of gym equipment or an outdoor playground the person who used before you may have the virus," Ms Berejiklian said.
"We recommend wiping it down, using your discretion. Councils may take up the opportunity to have extra provisions."
Travel to regional NSW is still off the table.
It comes as NSW's health minister says the best people can give their mums when visiting on Mother's Day is to keep them safe by maintaining social distance.
Brad Hazzard has implored people to take care when visiting their loved ones on Sunday during the ongoing coronavirus crisis.
"We don't have a vaccine. We don't have herd immunity, we don't have a large group through the population who have actually had this virus and are now immune," he told reporters on Sunday.
Western Australia has similarly announced they would be heading to stage two of restrictions from 18 May.
That means many cafes and restaurants would be able to serve up to 20 customers at one time.
"I understand this may be confusing but I urge all Western Australians to remain focused on what we are doing here," Premier Mark McGowan said.
Sporting clubs and running groups up to 20 people would also be allowed from 18 May onwards.
Mr McGowan said regional travel restrictions would also be eased, but the states hard border with other states and territories would remain in place.
People in Australia must stay at least 1.5 metres away from others.
Check your state’s restrictions on gathering limits. Testing for coronavirus is now widely available across Australia.
If you are experiencing cold or flu symptoms, arrange a test by calling your doctor or contact the Coronavirus Health Information Hotline on 1800 020 080.
The federal government's coronavirus tracing app COVIDSafe is available for download from your phone's app store. SBS is committed to informing Australia’s diverse communities about the latest COVID-19 developments.
News and information is available in 63 languages at sbs.com.au/coronavirus