Much of Australia woke to relaxed coronavirus measures on Monday, with millions urged to “get out of the house”.

But while intrastate travel is back on the agenda for many, heading beyond your home state remains off limits for at least the next several weeks for much of the country.

Queensland, whose border has been the subject of tension between political leaders, brought forward eased COVID-19 restrictions by almost two weeks on Monday.

That means Queenslanders can now travel across their state – and Premier Annastacia Palaszczuk urged them to do so.

“I’m encouraging Queenslanders to get out of the house, to get into their car, and to book accommodation somewhere in Queensland that you haven’t been before,” she said.

“There is so much to explore. I don’t know where to begin.”

But they won’t be holidaying interstate – and they certainly won’t be welcoming Australians from other states.

“Let me make it very clear, the border will remain closed for the month of June,” Ms Palaszczuk said.

Queensland reported no new coronavirus infections on Monday, and there are only five active cases in the state.

Tweet from @AnnastaciaMP

NSW also eased many measures on Monday. The state’s pubs, beauty salons and museums were permitted to reopen, and travel within NSW is being encouraged.

NSW had three new COVID-19 cases on Monday, all in returned overseas travellers.

The beleaguered Newmarch House, where 19 residents have died and more than 70 people have been infected, was finally declared free of the virus on Sunday.

• See NSW’s current coronavirus restrictions here

On the other side of the country, Premier Mark McGowan announced a $2 million program to encourage Western Australian residents to holiday at home.

WA has further relaxed regional travel restrictions but Mr McGown has ruled out creating a domestic travel bubble with South Australia and the Northern Territory. He said the hard border to Australians from interstate would also remain.

“The more that they push it, the more they increase the resolve of Western Australians to do the right thing by our citizens and by ourselves,” Mr McGowan said.

“We are thousands and thousands of kilometres away from the eastern states. We will make decisions that better reflect the reality of life, the protection of the health and the economy of Western Australia.”

• See the latest on WA’s virus measures here

WA reported one new coronavirus case on Monday (in a returned overseas traveller). It has 29 active cases, including 20 from the Al Kuwait live export ship that docked in Fremantle in late May.

In South Australia, residents are being encouraged to explore their own state with a $1.5 million ‘Welcome Back’ tourism campaign.

SA had no new coronavirus cases to report on Monday, but Premier Steven Marshall said borders would remain shut.

“South Australia is back open for business, the tills are ringing, the customers are coming back in and the employees are returning to work,” he said.

But Mr Marshall also cautioned that further progress was conditional on SA continuing to have few or no new cases of COVID-19 and if the high level of testing was maintained.

“We’re not going to go backwards in terms of the health outcomes,” he said.

Tweet from @TISouthAust

In Victoria, where borders have never been closed but there have been some of the country’s toughest restrictions, residents were able to return to cafes, restaurants, pubs and beauty salons on Monday.

The state had four new COVID-19 cases on Monday. One was at the Rydges on Swanston, the Melbourne hotel housing returned overseas travellers that is now linked to eight confirmed infections.

There were no new cases linked to the family outbreak in Keilor Downs, in Melbourne’s north-west. It has infected 13 people across two homes.

• See Victoria’s up-to-date virus measures here

Premier Daniel Andrews said the “cautious, steady approach” to easing virus measures would continue.

“It’s far from over. We’ve still got a long way to go, and it’s not a matter of going back to normal,” he said.

“And we have to find a COVID normal.”

“Hopefully Victorians understand that there are still rules, and there is still a way to go before we beat this thing, before we get to the other side of it. Then we’ll be able to ease many, many more restrictions.”