Around 2,900 staff who are members of the Unite union had been due to walk out this coming weekend from June 16-19 as part of a long-running dispute about pay and benefits.
However, Unite announced that talks will now be held at conciliation service Acas to try and reach an agreement with the carrier.
BA had said the crew’s pay and rewards are in line with competitors but Unite argued the action was about benefits not being reinstated for crew who took part in earlier industrial action.
There has so far been a total of 26 days of strike action since the beginning of January, a move which Unite claims, has seen 1,400 of its members having their staff benefits - including travel - taken away.
Unite said the cabin staff, who work on both short and long-haul routes, are paid less than other BA crew.
BA had branded the new strike "completely unnecessary" adding it "had reached a deal on pay, which Unite’s national officers agreed was acceptable,” BBC News reports.
Although Unite claimed the fresh industrial action had occurred because the airline had treated staff who had participated in earlier strike action unfairly.
"Punishing staff for using legitimate industrial means to reach a wage deal is a culture that Unite cannot accept," the union said.