Tony Woodley, the leader of the Unite union, told the BBC there had been a "catastrophic" breakdown in negotiations after left-wing protesters interrupted the talks Saturday.
Willie Walsh, the airline's chief executive, said he hoped the strike could be avoided but added he was angry because a Unite leader used Twitter to sidetrack Saturday's talks before a mediator.
The airline, which posted a record $611 million annual loss Friday, said contingency plans would enable most flights to continue but warned of delays and cancellations during the first of three planned strikes.
The BBC said more talks are unlikely Sunday but the union wanted to meet with the airline as soon as possible.
The walkout threat, though it comes amid a long dispute over pay and working conditions, is specifically a response to disciplinary action against some members and the removal of travel perks after March strikes, Unite told the BBC Sunday.
Walsh, however, called travel concessions and the disciplinary actions union "distractions" and said the airline's costs were at the center of the dispute.