Qantas says it has been losing A$15 million ($19.5 million) a week from industrial action.
The shock tactic of suspending all flights had affected 68,000 passengers by yesterday, with more than 100 planes grounded around the world.
Qantas' Australian competitor Virgin Blue added 3000 seats to its domestic network yesterday, while the long-haul budget airline AirAsia offered "rescue fares". "We have so far helped over 20,000 stranded Qantas passengers," a Virgin Australia spokeswoman said.
The Government is furious at Joyce, whose actions could disrupt federal Parliament, due to resume tomorrow after a two-week suspension. Seventeen world leaders attending the Commonwealth meeting in Perth have been forced to alter their travel plans.
Bill Shorten, the Assistant Treasurer, and a former union leader, condemned Joyce's "radical overreaction", calling it a "high- handed ambush of the passenger".
"I believe Australians want to see this dispute settled; I want to see it settled," Prime Minister Julia Gillard told reporters in Perth.
On Saturday, the Government called an emergency meeting of the Fair Work Australia tribunal, which was last night considering whether to order a suspension or permanent halt to the unions' strike action. Joyce said planes could be back in the air within hours of a decision.
That did not mollify American tourists Douglas and Diane Phillips, who were buckled in and awaiting take-off from Los Angeles to Melbourne when the pilot informed passengers that the flight had been grounded. "At first everyone thought they were kidding for some reason, but then we realised they were deadly serious," Phillips told Associated Press.
Members of the one-day cricket squad in South Africa - Doug Bollinger, Xavier Doherty, James Pattinson, Steve Smith and David Warner - were having transfers to get home as soon as possible.
The grounding could have a substantial dampening effect on the economy, analysts warned. In the short term, itwas almost certain the national carrier's dispute with unions will send ripples through the Australian sharemarket today. But if the stoush proves protracted, it could substantially hit the tourism and freight sectors, AMP chief economist Shane Oliver said. "These things can have quite a negative impact on an economy."
CommSec chief equities economist Craig James said many Qantas shareholders would reach for the "sell" button, sending the national carrier's share price even lower.
Joyce became the fourth most popular trend topic in Australia yesterday.
Unfortunately, many Twitter users homed in on an Alan Joyce of Stanford, California. The American acquired more than 300 extra Twitter followers in the past 24 hours after tweeters confused him with the Qantas boss. "Oh dear," he tweeted. "I think Australia is waking up again ... time to prepare for another deluge of tweets."
Joyce later tweeted that Qantas had contacted him "with a graceful apology", which could indicate not all his new followers were friendly.
Qantas itself was also a major topic on Twitter, with many tweeters expressing their disappointment with the airline's action.
Labor MP Mike Kelly tweeted: "Finding it increasingly difficult 2 accept credibility of Alan Joyce. Worried we will see the flying roo give way 2 the flying pig emblem."
- additional reporting AAP