The move was announced tonight following day-long discussions between leaders of the Transport and General Workers Union and representatives of almost 11,000 stewards and stewardesses.
The workers are due to walk out for 48 hours next Tuesday and Wednesday in a bitter dispute over sickness absence, pay and staffing.
Tony Woodley, general secretary of the Transport and General Workers Union, met BA's chief executive Willie Walsh yesterday and reported back to branch officials today.
The two sides said that fresh talks would be held tomorrow but time was running out to head off the strike.
BA has already cancelled all flights out of Heathrow and domestic and European flights out of Gatwick for the duration of the strike costing it millions of pounds in lost revenue.
