Unite said that after the completion of the strike this weekend, the union will be in a position to call a further strike period after the Easter holidays.
A spokeswoman from BA said the airline remained available for talks with the union.
The news comes in the middle of the second of two strike periods launched by BA staff this week.
The carrier said on Saturday that 63 per cent of cabin crew staff turned up to work and that it flew more than 60,000 customers on 470 flights.
Chief executive Willie Walsh said: “Despite the union's promises, this strike has affected the Easter holiday plans of thousands of hard-working people.”
BA also said that it plans to operate 70 per cent of long haul and 55 per cent of short haul flights out of Heathrow, while Gatwick and City airports remain untouched by the strike.
However, Unite yesterday said that 50 per cent of BA’s cabin crew scheduled to work are on strike and the airline is operating with only 15 per cent of its regularly scheduled staff.
Unite estimates that on a normal working day 2,100 crew are rostered to work, claiming the airline has significantly reduced the number of crew rostered to work.
The bitter dispute between BA and Unite has come under scrutiny by parliamentary figures recently, with Conservative party leader David Cameron condemning Prime Minister Gordon Brown for making the strike possible.
Cameron said that Brown’s inconsistent approach to the industrial action, along with failing to back non-strikers over the disputes brought him into the hand’s of the unions.
“I think the unions have scented weakness in the government and that's one of the reasons why we're seeing quite so many strikes,” said Cameron.
Brown responded by saying that the government wanted BA workers to be back at work.