BA has accused union leaders of failing to take up an offer of further talks in an effort to stop the five-day strike by cabin crew starting at midnight.
The airline said it was disappointed Unite had resorted to "negotiation through the media".
Earlier, Unite's joint general secretary Tony Woodley offered to call off the latest walkout if travel perks for cabin staff were reinstated.
But BA said it had already agreed to do so once its deal was accepted in full.
Talks were brought to an abrupt end on Saturday evening when left-wing protesters gatecrashed the venue where negotiations were being held.
Mr Woodley appealed to BA boss Willie Walsh via the media on Sunday afternoon, saying: "Willie, turn round and reinstate our people's travel, without unnecessary vindictive removal of their service, and this union will call off tonight's strike."
Unite says the removal of travel concessions for members who went on strike in March is one of the core reasons behind the latest series of four planned walkouts.
In response to Mr Woodley's comments, BA issued a statement calling on him to call off the strike and return to the negotiating table.
"We had agreed to a request from [conciliation service] Acas to meet this afternoon and are surprised that Unite did not take advantage of this," it said.
"We have already offered to reinstate travel concessions to cabin crew once all elements of our offer have been implemented.
"Of more concern to us is Tony Woodley's comment to the media that he wants to revisit certain proposals in our offer, when previously he had indicated that these were agreed."
The statement went on to again blame Bassa, the Unite branch representing crew, for the failure to reach an agreement.
Mr Walsh, BA's chief executive, had earlier told the BBC's Andrew Marr Show that he hoped the latest strikes could be averted.
However, he said he was angered by Unite's other joint leader, Derek Simpson, using Twitter to send out details of Saturday's talks before and during the interruption by the protesters.
"I was shocked and angry when I found out that Derek was doing that," he said.
"Sending out his version of events to the wider audience, that really did undermine my confidence in his desire to resolve this situation.
"It is a really serious issue."
Entries on Mr Simpson's Twitter page, dereksimpsonjgs, on Saturday included "Arguments over the 8 sacked workers," and "Fear of more sackings to come".
These were later followed by "If I have to apologise to Willy over twittering then I shall .... But I am not afraid of saying what is really going on... ".
Mr Woodley said Mr Walsh was wrong to focus on the Twitter issue.
"If Willie Walsh can travel to the Andrew Marr programme, and be on television [and] radio worrying about Twitter, when we can sort out the real issue of travel, along with the agreement and other things, I'll have to ask him to get his priorities right," he said.
Even if the strike is called off later on Sunday, BA's services next week are still likely to be affected, especially on Monday, as crews and planes may be in the wrong place.
BA has said that if the walkout does go ahead, it plans to fly more than 60,000 customers a day next week, operating 60% of long-haul flights and 50% of short-haul services from Heathrow.
It says all flights at London Gatwick and London City will operate as normal.
The airline is intending to lease as many as eight aircraft with pilots and crew from other UK or European carriers.
Earlier this week, BA was granted a court injunction preventing the strikes after the High Court ruled that the Unite union had not reported results of its strike ballot correctly to members.
However, this was overturned on Thursday following an appeal by the union.
In addition to the strike due to start at midnight, two further five-day walkouts by Unite members are scheduled to begin on 30 May and 5 June.
The long-running dispute between BA and Unite cabin crew members centres on jobs, pay and working conditions.
However, after striking workers had their travel concessions removed following the walkouts in March, with others facing disciplinary action, Unite said these issues also had to be addressed in any successful agreement.
Numerous BA cabin crew members rely on travel perks - where they pay 10% of normal fares - to commute to work from UK cities outside London, or even from mainland Europe.