NSW Health has confirmed the two cases of coronavirus in Albury, and diagnosed another case among a family member of the two.
NSW Premier Gladys Berejiklian said the cases were believed to have come from greater Melbourne, with one of the three having travelled there.
The other 11 cases diagnosed in NSW in the 24 hours to 8pm on Wednesday were all in hotel quarantine, but Ms Berejiklian said NSW was on high alert for seeding of cases from Victoria into NSW.
More than 400 residents had been tested, she said, urging others in border communities to be tested with the most mild symptoms.
NSW would not tighten its rules on gatherings or businesses for now, but it remained a possibility.
It would be a couple of weeks before it was clear whether the Victorian outbreak had made its way to NSW, but so far the signs were good, she said.
"What we find comforting is that in the last 24 hours 18,500 people did come forward to get testing. And given the extremely low rate of community transmission there is no science-based reason for us to change anything at this stage," Ms Berejiklian said.
"All I'm saying to everybody is please be on high alert. What we're doing is taking the science, taking the evidence and advice on a daily basis, and if we need to move on anything we will.
"At this stage there is no evidence to suggest we need to, but we won't know or a few weeks whether there has been any seeding ... community transmission bubbling away under the surface."
Ms Berejiklian supported the move to limit overseas arrivals, with the national cabinet considering a plan from Prime Minister Scott Morrison on Friday.
She also indicated that NSW could start charging international arrivals for their two-week hotel quarantine, saying they had had plenty of time to get back to Australia.
On Wednesday, Ms Berejiklian said if NSW had to begin hotel quarantine for NSW residents returning from Victoria, they would be sent the bill for the stay. On Thursday, she said international arrivals would be changed first.
Government figures on Wednesday showed that in month from June 7, 39,400 people have been quarantined in NSW, 15,400 in Victoria, 10,050 in Queensland, 5400 in Western Australia, 960 in the Northern Territory, 680 in South Australia, and 307 in the ACT.
Another 350 are due to arrive in Canberra in time to start university in two weeks, on July 27, under a pilot scheme to start bringing international students back.
But scant details have been released about the plan, and its status is unclear.
A fortnight ago the Australian National University said the students would come from a range of countries on one flight, but the departure city was yet to be confirmed.
Our COVID-19 news articles relating to public health and safety are free for anyone to access. However, we depend on subscription revenue to support our journalism. If you are able, please subscribe here. If you are already a subscriber, thank you for your support. If you're looking to stay up to date on COVID-19, you can also sign up for our twice-daily digest here.