The NSW government has "strongly recommended" all residents wear face masks, while use of covering is now mandatory in Victoria.
While not yet compulsory in NSW, Premier Gladys Berejiklian said residents should wear masks in public when social distancing could not be guaranteed, such as on public transport or in a grocery store.
Ms Berejiklian urged customer-facing staff to wear masks, as well as residents attending a place of worship and anyone in areas where there was high community transmission.
"I can't stress enough that the next few weeks will make or break us in terms of the way we get through this pandemic and that's why I'm urging everyone to take this advice," she said.
Albury MP Justin Clancy said he had spoken to Ms Berejiklian on Saturday and stressed to her the need for a "level of stability" on border clamps.
"It's been a challenging period for our communities and continuing to tighten things makes that more challenging," he said.
Mr Clancy did not answer directly when asked if he thought mask wearing would become compulsory in NSW.
"For me it really is about following the recommendations from the (NSW) chief health officer in that regard," he said.
"If our people can heed the call to wear masks where they can't socially distance, we need to be following that advice and encouragement because we want to make sure we do what we can to avoid further lockdown."
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Twelve new cases of COVID-19 were detected in NSW in the 24 hours to 8pm Sunday, while 671 new cases and seven deaths were recorded in Victoria.
Last week, Wesfarmers, the parent company of Woolworths, Big W, Dan Murphy's and BWS urged NSW residents to wear masks in stores.
As of today, mask use is mandatory south of the border with Victoria Police able to issue on-the-spot fines of $200 to people not wearing a face covering in public without a legitimate reason.
Mask makers like Sue Ellen Hillier of Sue Ellen Drapery in Yackandandah have been working all hours to keep up with demand since Victorian Premier Daniel Andrews' announcement on Thursday.
Mrs Hillier and three volunteers have been working from about 5am to 10pm to fill orders.
"Thursday was madness," she said. "That was my day off I went to town to visit ... the grandchildren, got a phone call and that was it, madness.
"It feels really good except it wears us out, in 39 years, this is the year."