Earlier in February, Treasurer Joe Hockey suggested the government could provide a debt guarantee to the ailing airline, as the edict about ending corporate welfare did not apply because it operated in a distorted market.
He said there was a "price to be paid by the community" for laws restricting Qantas' ability to operate freely.
Under the Qantas Sale Act, the airline must remain majority Australian-owned and keep its headquarters and key operations in Australia.
The airline, which on Thursday announced $2 billion in job cuts and other measures over three years, is seeking a debt guarantee to shore up its credit rating and a repeal of the act so it can seek foreign partners.
Mr Abbott told parliament this week that if the government provided a guarantee to Qantas, it would have to offer it to other airlines such as its key competitor, Virgin Australia.
The prime minister told reporters in Darwin on Friday that he and the treasurer had been in "regular dialogue" on the issue, which would continue.
"Qantas is an iconic Australian business," he said.
"It has been and should be one of the world's great airlines.
"The duty of government is to do everything we reasonably can to take the costs off Qantas and to allow it to compete on a level playing field with everyone else. That is why we are looking at changing the Qantas Sale Act."
Mr Abbott said Labor could ease pressure on Qantas by backing the change, as well as repealing the carbon tax.
We didn't get the answers we were after: Unions
Unions want outside experts to review Qantas's full operations to determine where cuts can be made, saying they don't believe the company's management has looked at all the issues.
Several union leaders have met with the airline's top brass on Friday for crisis talks following the announcement that 5000 jobs will be cut to meet a $2 billion cost savings target.
"They didn't feel that having an external provider or expert come in to conduct such a review," Transport Workers Union's Tony Sheldon said after the talks.
"They have indicated that there are a number of processes that are happening at the moment. And again we said you: 'You have to engage in proper consultation or not'."
As well as firing people, retiring old planes, slashing capital spending and axing some routes, Qantas has asked staff across the company to take a wage freeze.
"Before we're looking at issues of wages freeze, we want the company to come out with all the facts," ACTU national secretary Dave Oliver told reporters outside the meeting.
"One thing that we will suggest is agreeing to a review, where we can bring in some outside expertise to have a look at the full operation of the airline ... and see where we can get cost savings."
Mr Oliver wants to see management's plan for the airline's future.
"If they think they can secure the future of this airline by cutting jobs and cutting wages, well I think there are considerable problems," he said.
"We want this company to justify every job loss."
