The national carrier announced its shock decision to lock out union staff and cancel all flights indefinitely on Saturday, a move that left the country reeling and passengers scrambling for alternatives.
The travellers' fate lies in the hands of the regulator Fair Work Australia, which reconvened an emergency three-man panel Sunday.
It could potentially suspend strike action for as long as 120 days so talks can take place, or order a permanent termination to the industrial dispute and so permit Qantas to take to the skies again.
After Prime Minister Julia Gillard took the rare step of ordering in the workplace mediator, a government lawyer told the tribunal the grounding was costing Australia's economy "tens of millions" of dollars each hour.
Gillard appeared to agree with Qantas that the row should be ended with "certainty".
"The government... is seeking to bring industrial action to an end and to have the dispute resolved so we can proceed with certainty with our iconic airline Qantas," she said in Perth Sunday.
She added that the airline needed to function properly and in "circumstances where employees and Qantas know what the future holds for them".
Qantas chief executive Alan Joyce said earlier he too was seeking certainty and that his planes would fly again if the panel ordered a full termination of all industrial action.
"A termination stops the lockout," he said, adding that a mere suspension of the dispute was not good enough to settle a row tearing the 90-year-old airline apart.
Qantas said more than 68,000 passengers on 447 flights were affected by the grounding of 108 aircraft in 22 cities, with frustrated customers venting their anger at hubs from Europe to Asia and the US West Coast.