Bendigo Labor MHR Lisa Chesters was the party's first MP to urge the government to keep the higher rate of JobSeeker and Youth Allowance, rather than remove it after six months as planned.

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Ms Chesters, a member of the party's left faction, said the increased rate was recognition from the government that "the rate was previously too low", and that dropping it back after six months would harm both the long-term unemployed and those recently made unemployed by the COVID-19 crisis.

The $550 fortnightly supplement starts rolling out this week.

The matter has not been before Labor caucus.

Labor's formal position on JobSeeker, formerly Newstart, remains the same as their pre-election commitment to a review into the rate with a view to raising it, along with a review of associated issues in Australia's welfare system.

That appeared to be the views of Lyons MHR Brian Mitchell and Tasmanian senator Helen Polley.

Mr Mitchell said the supplement was "a good solution" as a "stop-gap", but the entire system needed to be reviewed.

"Anything that assists people to have a more liveable income would be welcomed," he said.

"What shape or form that would take, I don't know, given the way things are going keeping people on the higher JobSeeker would be at least a stop-gap measure until a more comprehensive analysis can be done.

"The whole system needs to be looked at properly."

Mr Mitchell said there would be a need for "a much more comprehensive income support system" post-virus, and he urged against an austerity budget to rein in government spending.

Senator Polley said it was too early to make predictions about post-virus Australia, as there was no way of knowing what the economy would look like at this stage.

"I'd love to be able to support that, but I think it's too soon to be able to even hazard a reliable intelligent guess at what our economy is going to look like coming out of this pandemic," she said.

"This is something the government is going to have to deal with when it takes that money away from people."