The Australian Council of Trade Unions had originally called for almost three million workers on minimum and award wages to receive a five per cent pay increase when the Fair Work Commission hands down its annual wage review in June.
But worsening inflation expectations caused by the war in the Middle East have prompted the peak union body to aim higher.
A six per cent wage rise would increase the minimum wage to $26.45 an hour and leave a full-time worker on the minimum wage $57 a week better off.
Workers are still behind where they were in 2021 and should not be allowed to go backwards further because of US President Donald Trump's war with Iran, ACTU secretary Sally McManus said.
She argued higher minimum and award wages did not lead to increased inflation because they were separate to the enterprise bargaining system.
"Ten per cent of the overall payroll is the minimum wage workers, and them getting a pay rise that keeps up with inflation, or a bit more, doesn't feed into anyone else's pay rise," she told reporters on Thursday.
AMP chief economist Shane Oliver disagreed, saying such an increase would be "disastrous" for inflation.
Award wages directly influence pay rise claims across the economy, he said.
The Fair Work Commission references its decision off quarterly inflation in March, which came in at 4.1 per cent.
Dr Oliver said an increase above inflation plus productivity growth of 0.8 per cent would lock in inflation expectations for businesses, which would pass on rising labour costs to consumers and households, who would demand higher pay rises, risking a wage-price spiral.
While the spike in inflation was caused by an oil supply shock, the demand side of the economy was already too high before the war, he said.
An extra $18 billion in federal government spending in the next financial year did little to take the pressure off the RBA, leading Dr Oliver to lock in his prediction for another rate rise.
"They're not raising interest rates because they think they can bring down global oil prices," he told AAP.
"They're trying to prevent higher underlying inflation from continuing and flowing on to inflation expectations."
Without nominating a specific number, the Albanese government previously recommended the commission hand down a "sustainable" pay rise above inflation.
The budget aimed to drive down headline inflation in the short term through $2.9 billion in temporary cuts to the fuel excise and heavy vehicle road user charge, but this still added to aggregate demand.
Two household surveys pointed to a drop in consumer spending in April of about one per cent, as a result of the temporary reduction in fuel prices.
Signs of a slowdown were emerging in discretionary spending, with travel down 9.3 per cent over the month, NAB transaction data showed.
"The spending side of the Australian economy needs to slow and households are forecast to do much of the heavy lifting on this front," Commonwealth Bank head of Australian economics Belinda Allen said.
The budget forecast household consumption growth to slow from 2.25 per cent this financial year to 1.75 per cent in 2026/27, as higher prices weighed on real incomes and spending.
Treasury's assumptions are based on the oil price gradually declining from about $US100 a barrel to $US80 a barrel by mid-2027.
Unless a resolution to the conflict is reached soon, CBA commodities analyst Vivek Dhar said oil prices would likely rise to about $US150 a barrel by mid-July.
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