The union was due to begin balloting on Tuesday unless there was a breakthrough in the dispute, which has seen 22 days of strike action since March.
BA welcomed Unite's move calling it "a genuine opportunity to end" the row.
BBC News - Unite union offers to postpone BA strike ballot
How does doing longterm damage to BA help anyone? The ongoing dispute is leaving BA's reputation in tatters. Interesting to see the PM flew to the G20 summit on Virgin... Maybe he was worried about having his flight cancelled as well

Is it time to clip Unites wings, or do people think anything good will come from this ongoing row?