The Transport Workers Union (TWU) rejected a new agreement proposed by Qantas for the air carrier's 3,800 baggage handlers, caterers and ground staff.

However, the Australian Licenced Aircraft Engineers Association (ALAEA) indicated it may likely sign a deal and end the union's labor dispute with Qantas when it meets airline representatives at Fair Work Australia on Thursday afternoon.

:"We've de-escalated our industrial action to show we are serious about these negotiations, and today's meeting will be an opportunity for Qantas to show they are equally serious about resolving the matter," ALAEA Federal Secretary Steve Purvinas said in a statement.

The engineers' strike has caused the grounding of seven jets and cancellation of 80 flights. As a result, a number of Qantas passengers have shifted to other air carriers with more reliable service.

The prolonged work stoppages by three unions had led Qantas Chief Executive Alan Joyce to warn that the strikes are placing 35,000 jobs in the flag carrier at risk.

"When we are forced to ground aircraft it means we have fewer flights, less passengers and if it gets worse it could mean we need less people employed at Qantas," Mr Joyce said in a statement.

Short of directly intervening into the labor row, Prime Minister Julia Gillard urged Qantas unions and management to settle the problem.

"I am concerned about its impact on Qantas itself, on other businesses and of course on passengers.... My message remains to the parties. 'Get around a table and get this fixed,'" Ms Gillard said.

Meanwhile, a leading independent online air ticket vendor urged Ms Gillard to step into the Qantas labor problem. Webjet Chairman David Clark wrote a strongly worded letter to the prime minister because of the labor row's impact on the travel industry.

Transport Minister Anthony Albanese has warned that provisions in the Fair Work Australia Act allow the government to intervene if the labor problem becomes a threat to national economic interest.

"I think both sides in the dispute need to apply a bit of common sense, need to be flexible, and need to get this agreement done," Mr Albanese said.

Following the TWU rejection of the deal, the union said union members in Brisbane and Melbourne would stop working for one hour on Tuesday to attend meetings on their next course of action.