The union says it will consult BA crew members on the latest offer from the airline.
But the union warned that it was not in a position to recommend the BA proposal to members because it did not fully reinstate staff travel arrangements stripped from crew who took lawful industrial strike action in March and May.
The latest offer, tabled on Friday, included new "top-up" payments for staff, as well as guaranteed rises in basic salary for two years from 2011.
Unite joint general secretary Tony Woodley said it would be "inexplicable" not to put the new offer to members, and said BA had made it clear the new offer would be removed if the fresh strike ballot, to take place on June 29, went ahead.
"As a consequence of the company's last and final offer the union and its representatives will have no choice but to delay our vote in order to allow our members to consult on the offer", said Woodley. But he added that the "Failure by BA to restore travel in full means the possibility of a recommendation nil and makes acceptance of the offer uncertain."
BA crew members have so far staged 22 days of strike action this year, while the carrier's CEO Willie Walsh has said the airline expects to operate 100 per cent of BA's long-haul schedule should a fresh wave of strikes become a reality.