Unite said there was little hope of a breakthrough in its bitter cabin crew dispute with British Airways, despite agreeing to postpone a strike ballot.
Tony Woodley, Unite joint leader, said the failure of BA to reinstate staff travel arrangements to crew who took part strike action in March and May meant any deal was "uncertain".
The union said there was "nil" chance that it would recommend the latest offer from the airline to its members.
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 failure to restore staff travel arrangements - which include the chance to buy discounted flights - remained a major obstacle.
"The fact that staff travel arrangements have not been restored to thousands of crew prevents this offer from BA being the breakthrough everyone seeks," he said.
"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.
The new offer includes a top-up payment to guarantee that existing crew will not lose out on route allowances when newly-recruited crew begin flying in the autumn.
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."
During the days of the dispute, BA had been able to fly most of its long-haul routes but had to axe a number of short-haul flights.
The strike ballot starting on Tuesday would have taken around a month and would have led to the possibility of walkouts in the busy travel month of August
Transport Secretary Philip Hammond said: "Any movement in this increasingly acrimonious dispute is welcome after months of stalemate.
"But the real test must now be progress towards an enduring solution that will remove the threat of industrial action from BA, allowing it to rebuild its brand image and restore the confidence of its passengers.
"That is the only way to ensure both the future of the airline and the tens of thousands of jobs that depend upon it."Reuse content