Tony Woodley, the joint leader of Unite, the union representing striking cabin crew, called on Monday for talks with the airline in an attempt to end the row, which he said had cost BA millions of pounds.
Addressing a rally of striking union members at a football ground near Heathrow airport, said "the economics of the madhouse should now be put to one side.
"We need to reach a sensible, fair deal, to get this company up and running again, to get passengers flying again, to get all of the planes off the ground."
Unite and BA have both claimed victory over the walkout that has caused the airline to cancel over half its 1,950 flights normally scheduled over the period.
BA reported that nearly 98 per cent of staff reported for work at Gatwick airport and more than half showed up at Heathrow, allowing it to reinstate a number
of cancelled flights.
But Unite said that only 300 of its 2,200 cabin crew scheduled to work over the weekend turned up, and accused the airline of counting inbound crew to inflate the numbers of staff on duty.
BA stressed that it was legally obliged, as a listed company, to release accurate figures.
The strike is also bad news for the ruling Labour party, which relied on funding from the country's labour unions, ahead of elections expected in six week's time.
'Winter of discontent'
The opposition Conservative party is seeking to evoke memories of the difficulties the Labour government had in the 1970s, culminating in the mass strikes that became known as the "winter of discontent" and led to the election of Margaret Thatcher.
The action went ahead on Saturday after last-ditch the previous day collapsed amid accusations from the Unite union that management was not interested in finding an agreement with cabin crew.
The airline wants to save more than $90m annually through a series of cuts to pay and staffing to help cope with a fall in demand, volatile fuel prices and increased competition from low-cost carriers.
Unite argues it was not properly consulted on the changes.
BA says it had offered to modify the changes, even though they had been approved by Britain's high court, but Unite had declined to put the offer to its members to vote.
Unite has a second four-day walkout planned to begin on March 27 and has said more strikes will be scheduled for after April 14 if the dispute is not resolved.