Prime Minister Anthony Albanese has lodged a submission to the commission, calling for a pay rise for Australia's lowest paid workers.
However, the submission did not include a figure as to how much the minimum wage should be increased.
During the election campaign, Mr Albanese backed a rise of 5.1 per cent to the minimum wage in order to keep up with rising inflation levels.
Mr Dutton, who is expected to be named as opposition leader next week, said the government had broken election promises.
"Anthony Albanese looked Australian workers in the eye and said that he would absolutely support the 5.1 per cent increase in wages," he said.
"He looked workers in the eye and he has lied to workers."
Deputy Prime Minister Richard Marles defended the government's decision not to include an exact figure as to how much the minimum wage should rise.
"The focus of the submission is what we have argued throughout this election campaign ... That is, those on the minimum wage should not be left behind," he told reporters in Melbourne on Friday.
"Those who are on the minimum wage should not receive a real wage cut."
The submission was lodged to the Fair Work Commission on Friday, but has yet to be made publicly available.
Mr Marles said it was important the government use its voice to argue for the wage increase.
"We are experiencing in Australia a cost of living crisis because of the failures of the former Liberal government," he said.
"We see that with rising power prices, with rising petrol prices."
One week on from the federal election, the prime minister has spoken to French President Emmanuel Macron for the first time.
The two leaders agreed to rebuild a bilateral agenda after relations soured over the Morrison government's decision to ditch a submarine contract with France.
Meanwhile, Foreign Minister Penny Wong has used a visit to Fiji to pledge Australia's support in the Pacific region.
Mr Albanese said support would be the first step and Australia could differentiate its offering to the Pacific from what China has pledged.
"What we can offer is no strings attached and that's the big difference," Mr Albanese said.
"We can offer respect for the sovereignty of our Pacific island neighbours. We can offer the long-term support and relationships that Australia has with our Pacific island neighbours."
