The prime minister is working on welfare reform and urging states to open their borders as he seeks to deal with huge job losses as a result of the coronavirus.

As the coronavirus throws hundreds of thousands more people out of work, Scott Morrison is working out how to reshape Australia's welfare system.

The prime minister also continues to agitate to unlock interstate travel, with new figures showing ongoing border closures are costing the economy $84 million a day.

Australia's unemployment rose to 7.1 per cent in May as another 227,000 people lost their jobs.

The latest jobless figures are the worst since October 2001 and would be far grimmer were it not for another big fall in workforce participation.

Mr Morrison described the figures as heartbreaking.

He also warned there would likely be more people joining unemployment queues in the months ahead.

The government is examining the best way to balance its JobKeeper wage subsidy and doubling of the JobSeeker unemployment payment beyond their scheduled September finish.

Earlier in the week, Industrial Relations Minister Christian Porter conceded it was inevitable people would move from the wage subsidy to unemployment payments.

Mr Morrison and Treasurer Josh Frydenberg rejected questions from Labor in parliament about how many more jobs would be lost once JobKeeper ends.

"The member's question is presumptuous because he makes assumptions about government policy on decisions that have not been made," the prime minister told parliament.

Earlier, he didn't rule out an increase to the dole's $40-a-day base rate, which the government is reportedly tossing up.

The Northern Territory government announced on Thursday it will reopen its domestic borders on July 17.

South Australia is already allowing visitors from the NT, Western Australia and Tasmania, and will open up to other states on July 20 while Queensland plans to reopen from July 10.

WA and Tasmania have not said when they will loosen travel restrictions.

Mr Morrison said borders should never have been closed in the first place.

There were 21 new cases of coronavirus recorded across Australia on Thursday.

Victoria had another big jump with 18 new cases, including a third Black Lives Matter rally participant testing positive.

NSW recorded two and WA one, all returned travellers in quarantine.