Western Australian Premier Mark McGowan has urged NSW to do more to “crush and kill” COVID as another round of border tensions flares across the country.

NSW remains the focus of the toughest interstate border rules as it confirmed five more local coronavirus cases on Monday – including two whose origins remain a mystery.

Mr McGowan said NSW should be aiming to eliminate “the virus from Sydney” so all of Australia “could rest a lot easier”.

“There’s five states and two territories doing one thing, and one state doing something different. I go with the majority,” he said.

“The states and territories that want to eliminate the virus, I think, have the right approach. The idea that you tick along with the virus and somehow that is a better model is wrong.

“I just urge the NSW government and people in NSW to look outside of NSW [to] what other states and territories are doing in order to crush and kill the virus.”

One of NSW’s new mystery cases is a man in his 40s who went to a western Sydney hospital on Saturday night. His infection was confirmed after 8pm Sunday and he will be officially included in Tuesday’s case numbers.

The other case is one of his household contacts. NSW authorities were racing on Monday to try to link the infections to an existing outbreak.

In the meantime, Premier Gladys Berejiklian fired back at criticism of the NSW approach to fighting the virus, urging other state and territory leaders to “do better” on border closures.

“As premier of this state, I would love to have had input and say rather than closing all of NSW or Sydney from a particular state, please just consider the northern beaches or give us 24 hours to get back to you on how we can manage this,” she said.

“As leaders, and again I include myself in this, all of us can and should do better when it comes to borders because it affects thousands of people, sometimes hundreds of thousands of people when multiple border changes are happening around the nation.”

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Victoria announced on Monday that it would reopen its borders to regional NSW from midnight. Restrictions on travel from greater Sydney will remain.

The state unveiled a three-step “traffic light” system for travel into Victoria. All travellers will require permits, whether they come from unrestricted green areas will allow unrestricted travel or restricted orange zones. Travel will be barred from red zones – such as greater Sydney.

Police will remain at entry points to Victoria.

Premier Daniel Andrews said regional NSW would be declared an orange zone – allowing Victorians trapped in country areas of the state after the abrupt New Year’s Eve border closure to come home.

Victorian chief health officer Brett Sutton said the risks in travelling interstate amid the pandemic were clear.

“We are all in need of seeing family and friends and loved ones, that is important,” he said.

“People get caught out. Sometimes it is an inconvenience and sometimes it is tragic, [but] people need to bear in mind that that is a risk that we are all needing to manage in our lives.

“I totally understand people’s need to travel interstate and they need to make that choice for themselves, but they need to recognise there is always a risk that is present.”

Under Victoria’s system, greater Brisbane also remains a red zone. That is despite Queensland Premier Annastacia Palaszczuk announcing the end of the city’s snap three-day lockdown from Monday night after a third consecutive day without local virus infections.

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The Northern Territory and the ACT announced on Monday afternoon that they would drop their hotspot declarations for Brisbane, allowing a return of quarantine-free travel.

NT Chief Minister Michael Gunner confirmed the move on Monday.

“[In] terrific news from Queensland, there has been no community transmission of the concerning positive case last Friday. The doctors’ advice this morning is the greater Brisbane area no longer presents a risk to the territory,” he said.

“For greater Sydney, there is no change to the hot spots. The doctor’s team will monitor that and hopefully some good news there is not too far away.”