Unite said there was little hope of a breakthrough on Sunday in its bitter cabin crew dispute with British Airways, despite agreeing to postpone a strike ballot.
The union said there was "nil" chance that it would recommend the latest offer from the airline to its members.
Tony Woodley, Unite joint leader, said the failure of BA to reinstate staff travel arrangements, which include the chance to buy discounted flights, to crew who took part strike action in March and May meant any deal was "uncertain".
BA made the new offer on Friday, which includes two years of guaranteed rises in basic salary from February 2011.
A spokesman for the airline said it welcomed Unite's decision to delay the strike ballot.
He added: "We believe our offer is fair and reasonable and provides a genuine opportunity to end this dispute."
Mr Woodley said it would be "inexplicable" not to put the offer to union members.
But he added: "The fact that staff travel arrangements have not been restored to thousands of crew prevents this offer from BA being the breakthrough everyone seeks. Failure by BA to restore travel in full means the possibility of a recommendation is nil and makes acceptance of the offer uncertain."
Unite had been due to hold a ballot starting next Tuesday unless there was a breakthrough in the dispute, which has seen 22 days of strike action since March and cost BA around £150 million.
Making the offer on Friday, BA's cabin crew head Bill Francis said: "We have changed our offer in line with feedback we have received from crew and we genuinely believe that it can end this dispute - which is what the vast majority of crew and our customers want."
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