Social Services Minister Amanda Rishworth has ruled out a lift in unemployment benefits in the October budget, citing fiscal constraints.
But the Greens say allowing people to remain in poverty is a political choice.
Australia's peak welfare group wants the JobSeeker payment rate to be lifted from $46 to $70 a day.
The Australian Council of Social Service has received the backing of independent senator David Pocock, who argues providing extra money for the unemployed makes more sense than tax cuts for the wealthy.
Ms Rishworth told ABC Radio on Tuesday the government was being "very clear" about JobSeeker.
"At the moment, in the October budget, this is not something that we're going to proceed with," she said.
"We'll assess it budget by budget ... that's the challenge of inheriting a trillion dollars worth of debt."
Yet the government's stance is "absurd" and "hypocritical", Greens senator Janet Rice said.
"Labor can find plenty of room in the budget to give billions in welfare to people like Clive Palmer, but nothing for job seekers," she said in a statement.
"Here's an idea: instead of handing out over $243 billion in stage three tax cuts for the rich, raise the rate of income support payments for people living in poverty."
The Greens want the government to commit to a livable income guarantee and raise the welfare rate to $88 a day, above the poverty line.
Ms Rishworth said she would continue to work with ACOSS and other organisations to get rid of barriers to employment.
She looked forward to progressing a number of ideas at this week's jobs and skills summit in Canberra.
The government was committed to the stage three tax cuts due to come into force in 2024, the minister said.
